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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': -2, 'Lhash': '1603442139222589459735342660173', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896257, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 72.86489866755561, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1, 3]], [31, [1, 4, 26, -31]]], 'bad_primes': [2, 3, 31], 'central_character': '1142784.1', 'coefficient_field': '1.1.1.1', 'conductor': 1142784, 'conductor_radical': 186, 'degree': 4, 'euler_factors': [[1], [1, -1, 3], [1, 0, -1, 0, 25], [1, -1, 12, -7, 49], [1, 0, 11, 0, 121], [1, -3, 8, -39, 169], [1, 0, 22, 0, 289], [1, 1, 18, 19, 361], [1, 0, -25, 0, 529], [1, 0, 4, 0, 841], [1, 4, 26, -31], [1, 9, 64, 333, 1369], [1, 0, 9, 0, 1681], [1, -2, 78, -86, 1849], [1, 0, -10, 0, 2209], 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-0.03320420028947896, 0.8950838761197014, 1.7838489449496384, 2.5015576298943185, 2.931202792259699, 2.9877284013827596], 'positive_zeros': ['1.26489281741664755971311219615534', '1.91097765562853954472273704087191', '2.48932756091283111397588211069667', '3.24084459906268147169457614140081', '3.48465830993130161851242594784524', '4.08552887414332821773601851516382', '4.63692943221780377838055091210131', '5.27259666667352935116883900228364', '5.49113311877190080836796921283313', '6.21327324192910162941231483790801', '6.38168043282382556604658362115461', '7.09351010203907541383746147180556', '7.42830552079449870980719386312566', '7.932364995635833004904834931728696'], 'prelabel': '4-1142784-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.9216594388205688, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 712190972385833652, 'z1': {'__RealLiteral__': 0, 'data': '1.26489281741664755971311219615534', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.91097765562853954472273704087191', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.48932756091283111397588211069667', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 72.86489866755561, 'bad_primes': [2, 3, 31], 'central_character': '1.1', 'conductor': 1142784, 'conductor_radical': 186, 'degree': 4, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, 1, 0, -2, 0, 0, 0, 3, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, -5, 0, 0, 0, -4, 0, 0, 0, 0, 0, -9, 0, 3, 0, 0, 0, 2, 0, 0, 0, 0, 0, -11, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 9, 0, -2, 0, 0, 0, -6, 0, 0, 0, 0, 0, -11, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, -4, 0, 0, 0, -6, 0, 0, 0], 'euler11': [1, 0, 11, 0, 121], 'euler13': [1, -3, 8, -39, 169], 'euler17': [1, 0, 22, 0, 289], 'euler19': [1, 1, 18, 19, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -25, 0, 529], 'euler29': [1, 0, 4, 0, 841], 'euler3': [1, -1, 3, 0, 0], 'euler31': [1, 4, 26, -31, 0], 'euler37': [1, 9, 64, 333, 1369], 'euler41': [1, 0, 9, 0, 1681], 'euler43': [1, -2, 78, -86, 1849], 'euler47': [1, 0, -10, 0, 2209], 'euler5': [1, 0, -1, 0, 25], 'euler53': [1, 0, -74, 0, 2809], 'euler59': [1, 0, -58, 0, 3481], 'euler61': [1, -9, 130, -549, 3721], 'euler67': [1, 6, 94, 402, 4489], 'euler7': [1, -1, 12, -7, 49], 'euler71': [1, 0, 100, 0, 5041], 'euler73': [1, 11, 170, 803, 5329], 'euler79': [1, -1, 102, -79, 6241], 'euler83': [1, 0, 35, 0, 6889], 'euler89': [1, 0, 12, 0, 7921], 'euler97': [1, 6, 154, 582, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -1, 3, 0, 0], [1, 0, -1, 0, 25], [1, -1, 12, -7, 49], [1, 0, 11, 0, 121], [1, -3, 8, -39, 169], [1, 0, 22, 0, 289], [1, 1, 18, 19, 361], [1, 0, -25, 0, 529], [1, 0, 4, 0, 841], [1, 4, 26, -31, 0], [1, 9, 64, 333, 1369], [1, 0, 9, 0, 1681], [1, -2, 78, -86, 1849], [1, 0, -10, 0, 2209], [1, 0, -74, 0, 2809], [1, 0, -58, 0, 3481], [1, -9, 130, -549, 3721], [1, 6, 94, 402, 4489], [1, 0, 100, 0, 5041], [1, 11, 170, 803, 5329], [1, -1, 102, -79, 6241], [1, 0, 35, 0, 6889], [1, 0, 12, 0, 7921], [1, 6, 154, 582, 9409]], 'index': 8, 'instance_types': ['ECNF', 'BMF', 'BMF', 'ECNF'], 'instance_urls': ['EllipticCurve/2.0.3.1/126976.1/f', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/126976.1/f', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/126976.2/g', 'EllipticCurve/2.0.3.1/126976.2/g'], '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': '4-1142784-1.1-c1e2-0-8', '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': '4-1142784-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.9216594388205688, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 712190972385833652, 'z1': {'__RealLiteral__': 0, 'data': '1.26489281741664755971311219615534', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9703542
{'Lhash': '1603442139222589459735342660173', 'Lhash_array': ['1603442139222589459735342660173'], 'label': '4-1142784-1.1-c1e2-0-8', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/126976.2/g'}
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id: 9703429
{'Lhash': '1603442139222589459735342660173', 'Lhash_array': ['1603442139222589459735342660173'], 'label': '4-1142784-1.1-c1e2-0-8', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/126976.2/g'}
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id: 9703279
{'Lhash': '1603442139222589459735342660173', 'Lhash_array': ['1603442139222589459735342660173'], 'label': '4-1142784-1.1-c1e2-0-8', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/126976.1/f'}
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id: 9703278
{'Lhash': '1603442139222589459735342660173', 'Lhash_array': ['1603442139222589459735342660173'], 'label': '4-1142784-1.1-c1e2-0-8', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/126976.1/f'}