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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': 0, 'A8': 0, 'A9': 1, 'Lhash': '1256759327132750999402130332004', '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': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 333.29080413713064, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, 0, 5]], [11, [1, -4, 11]]], 'bad_primes': [2, 3, 5, 11], 'central_character': '5227200.1', 'coefficient_field': '1.1.1.1', 'conductor': 5227200, 'conductor_radical': 330, 'degree': 4, 'euler_factors': [[1], [1, 1], [1, 0, 5], [1, 0, 4, 0, 49], [1, -4, 11], [1, 0, 16, 0, 169], [1, 0, -4, 0, 289], [1, 0, -10, 0, 361], [1, -4, 46, -92, 529], [1, 0, 38, 0, 841], [1, -8, 78, -248, 961], [1, -2, 66, -74, 1369], [1, 0, 62, 0, 1681], [1, 0, -4, 0, 1849], [1, 16, 142, 752, 2209], [1, 2, -14, 106, 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-1.4190915763593301, -2.3494875696169237, -3.2772631801172944], 'positive_zeros': ['0.991408300446891656385657480292172', '1.45896191837315043467382601463451', '2.05819683239581432452136057539636', '2.80106838852475612540391021741508', '3.23066597332443980701345432846191', '3.77279415780071677436228264553275', '4.26483165984210633367059547512495', '4.53661157539686235655561042088205', '5.09288483700304703580687720383734', '5.43620010668972877659421102934697', '5.95789367429028619689585123867611', '6.41176650308245350999104202909215', '6.59060614834756228025102481824180', '6.92318812947709829857199933576527'], 'prelabel': '4-5227200-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.272733766143977, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 783784963611473345, 'z1': {'__RealLiteral__': 0, 'data': '0.991408300446891656385657480292172', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '1.45896191837315043467382601463451', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.05819683239581432452136057539636', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 333.29080413713064, 'bad_primes': [2, 3, 5, 11], 'central_character': '1.1', 'conductor': 5227200, 'conductor_radical': 330, 'degree': 4, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -5, 0, -1, 0, 0, 0, 8, 0, -4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, -4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -24, 0, 0, 0, 5, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -8, 0, 0, 0, 14, 0, 4, 0], 'euler11': [1, -4, 11, 0, 0], 'euler13': [1, 0, 16, 0, 169], 'euler17': [1, 0, -4, 0, 289], 'euler19': [1, 0, -10, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -4, 46, -92, 529], 'euler29': [1, 0, 38, 0, 841], 'euler3': [1, 1, 0, 0, 0], 'euler31': [1, -8, 78, -248, 961], 'euler37': [1, -2, 66, -74, 1369], 'euler41': [1, 0, 62, 0, 1681], 'euler43': [1, 0, -4, 0, 1849], 'euler47': [1, 16, 142, 752, 2209], 'euler5': [1, 0, 5, 0, 0], 'euler53': [1, 2, -14, 106, 2809], 'euler59': [1, -16, 166, -944, 3481], 'euler61': [1, 0, 10, 0, 3721], 'euler67': [1, 0, 118, 0, 4489], 'euler7': [1, 0, 4, 0, 49], 'euler71': [1, 24, 286, 1704, 5041], 'euler73': [1, 0, 136, 0, 5329], 'euler79': [1, 0, -82, 0, 6241], 'euler83': [1, 0, 104, 0, 6889], 'euler89': [1, -4, 82, -356, 7921], 'euler97': [1, -14, 122, -1358, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 1, 0, 0, 0], [1, 0, 5, 0, 0], [1, 0, 4, 0, 49], [1, -4, 11, 0, 0], [1, 0, 16, 0, 169], [1, 0, -4, 0, 289], [1, 0, -10, 0, 361], [1, -4, 46, -92, 529], [1, 0, 38, 0, 841], [1, -8, 78, -248, 961], [1, -2, 66, -74, 1369], [1, 0, 62, 0, 1681], [1, 0, -4, 0, 1849], [1, 16, 142, 752, 2209], [1, 2, -14, 106, 2809], [1, -16, 166, -944, 3481], [1, 0, 10, 0, 3721], [1, 0, 118, 0, 4489], [1, 24, 286, 1704, 5041], [1, 0, 136, 0, 5329], [1, 0, -82, 0, 6241], [1, 0, 104, 0, 6889], [1, -4, 82, -356, 7921], [1, -14, 122, -1358, 9409]], 'index': 66, 'instance_types': ['ECNF', 'BMF', 'ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.11.1/43200.9/i', 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/43200.9/i', 'EllipticCurve/2.0.11.1/43200.4/i', 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/43200.4/i'], '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': '4-5227200-1.1-c1e2-0-66', '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': '4-5227200-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.272733766143977, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 783784963611473345, 'z1': {'__RealLiteral__': 0, 'data': '0.991408300446891656385657480292172', 'prec': 117}}
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lfunc_instances • Show schema
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id: 9933878
{'Lhash': '1256759327132750999402130332004', 'Lhash_array': ['1256759327132750999402130332004'], 'factors': ['4-5227200-1.1-c1e2-0-66'], 'label': '4-5227200-1.1-c1e2-0-66', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/43200.4/i'}
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id: 9933876
{'Lhash': '1256759327132750999402130332004', 'Lhash_array': ['1256759327132750999402130332004'], 'factors': ['4-5227200-1.1-c1e2-0-66'], 'label': '4-5227200-1.1-c1e2-0-66', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.11.1/43200.4/i'}
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id: 9933535
{'Lhash': '1256759327132750999402130332004', 'Lhash_array': ['1256759327132750999402130332004'], 'factors': ['4-5227200-1.1-c1e2-0-66'], 'label': '4-5227200-1.1-c1e2-0-66', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/43200.9/i'}
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id: 9933425
{'Lhash': '1256759327132750999402130332004', 'Lhash_array': ['1256759327132750999402130332004'], 'factors': ['4-5227200-1.1-c1e2-0-66'], 'label': '4-5227200-1.1-c1e2-0-66', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.11.1/43200.9/i'}