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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -3, 'Lhash': '1540915917830128964477185679557', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 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': 84.91111175372409, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, 3]], [17, [1, 3, 17]]], 'bad_primes': [2, 3, 17], 'central_character': '1331712.1', 'coefficient_field': '1.1.1.1', 'conductor': 1331712, 'conductor_radical': 102, 'degree': 4, 'euler_factors': [[1], [1, 0, 3], [1, 0, -2, 0, 25], [1, 0, 8, 0, 49], [1, -6, 27, -66, 121], [1, 0, 22, 0, 169], [1, 3, 17], [1, -5, 44, -95, 361], [1, 0, -7, 0, 529], [1, 0, -24, 0, 841], [1, 0, 38, 0, 961], [1, 0, -45, 0, 1369], [1, 17, 148, 697, 1681], [1, -5, 20, -215, 1849], [1, 0, 23, 0, 2209], [1, 0, -2, 0, 2809], [1, -8, 130, -472, 3481], [1, 0, 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0.11980572343116083], 'positive_zeros': ['1.21556832580894178017149313291987', '1.66891552653535809808405483050605', '2.59746762026882187511633433361102', '3.04793409085581096637883901884814', '3.68206459341817329010729748693317', '3.93541891434438593703303431891558', '4.74859736488083006510501884481257', '4.98914149416235335219451536452667', '5.64981632788892622516696634359094', '5.99267087202173280471535940029230', '6.56026162937724950267572356624602', '6.83370510301691614082835539748940', '7.15758741811198390223974129170217', '7.85230633966006796404025398235552'], 'prelabel': '4-1331712-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.035576148666708, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 912256611787836670, 'z1': {'__RealLiteral__': 0, 'data': '1.21556832580894178017149313291987', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.66891552653535809808405483050605', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.59746762026882187511633433361102', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 84.91111175372409, 'bad_primes': [2, 3, 17], 'central_character': '1.1', 'conductor': 1331712, 'conductor_radical': 102, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, -3, 0, 6, 0, 0, 0, 0, 0, -3, 0, 5, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -17, 0, 5, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -13, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 9, 0, 9, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -18, 0, -18, 0], 'euler11': [1, -6, 27, -66, 121], 'euler13': [1, 0, 22, 0, 169], 'euler17': [1, 3, 17, 0, 0], 'euler19': [1, -5, 44, -95, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -7, 0, 529], 'euler29': [1, 0, -24, 0, 841], 'euler3': [1, 0, 3, 0, 0], 'euler31': [1, 0, 38, 0, 961], 'euler37': [1, 0, -45, 0, 1369], 'euler41': [1, 17, 148, 697, 1681], 'euler43': [1, -5, 20, -215, 1849], 'euler47': [1, 0, 23, 0, 2209], 'euler5': [1, 0, -2, 0, 25], 'euler53': [1, 0, -2, 0, 2809], 'euler59': [1, -8, 130, -472, 3481], 'euler61': [1, 0, 94, 0, 3721], 'euler67': [1, 13, 174, 871, 4489], 'euler7': [1, 0, 8, 0, 49], 'euler71': [1, 0, -131, 0, 5041], 'euler73': [1, 14, 186, 1022, 5329], 'euler79': [1, 0, 146, 0, 6241], 'euler83': [1, -9, 186, -747, 6889], 'euler89': [1, -1, 106, -89, 7921], 'euler97': [1, 18, 259, 1746, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 3, 0, 0], [1, 0, -2, 0, 25], [1, 0, 8, 0, 49], [1, -6, 27, -66, 121], [1, 0, 22, 0, 169], [1, 3, 17, 0, 0], [1, -5, 44, -95, 361], [1, 0, -7, 0, 529], [1, 0, -24, 0, 841], [1, 0, 38, 0, 961], [1, 0, -45, 0, 1369], [1, 17, 148, 697, 1681], [1, -5, 20, -215, 1849], [1, 0, 23, 0, 2209], [1, 0, -2, 0, 2809], [1, -8, 130, -472, 3481], [1, 0, 94, 0, 3721], [1, 13, 174, 871, 4489], [1, 0, -131, 0, 5041], [1, 14, 186, 1022, 5329], [1, 0, 146, 0, 6241], [1, -9, 186, -747, 6889], [1, -1, 106, -89, 7921], [1, 18, 259, 1746, 9409]], 'index': 20, 'instance_types': ['ECNF', 'ECNF', 'BMF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.8.1/20808.1/b', 'EllipticCurve/2.0.8.1/20808.9/c', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/20808.9/c', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/20808.1/b'], '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': '4-1331712-1.1-c1e2-0-20', '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': '4-1331712-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.035576148666708, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 912256611787836670, 'z1': {'__RealLiteral__': 0, 'data': '1.21556832580894178017149313291987', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9831006
{'Lhash': '1540915917830128964477185679557', 'Lhash_array': ['1540915917830128964477185679557'], 'label': '4-1331712-1.1-c1e2-0-20', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/20808.1/b'}
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id: 9830716
{'Lhash': '1540915917830128964477185679557', 'Lhash_array': ['1540915917830128964477185679557'], 'label': '4-1331712-1.1-c1e2-0-20', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/20808.9/c'}
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id: 9830714
{'Lhash': '1540915917830128964477185679557', 'Lhash_array': ['1540915917830128964477185679557'], 'label': '4-1331712-1.1-c1e2-0-20', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/20808.9/c'}
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id: 9830702
{'Lhash': '1540915917830128964477185679557', 'Lhash_array': ['1540915917830128964477185679557'], 'label': '4-1331712-1.1-c1e2-0-20', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/20808.1/b'}