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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': 1, 'A8': 0, 'A9': -4, 'Lhash': '1323486695806486458415669823543', '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': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [-1.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 89.57942739416335, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, -1]]], 'bad_primes': [2, 7], 'central_character': '1404928.1', 'coefficient_field': '1.1.1.1', 'conductor': 1404928, 'conductor_radical': 14, 'degree': 4, 'euler_factors': [[1], [1, 0, 4, 0, 9], [1, 0, -2, 0, 25], [1, -1], [1, -2, 22, -22, 121], [1, 0, -14, 0, 169], [1, 0, 10, 0, 289], [1, 0, 28, 0, 361], [1, 6, 54, 138, 529], [1, 6, 66, 174, 841], [1, 0, 18, 0, 961], [1, -2, 26, -74, 1369], [1, 0, 34, 0, 1681], [1, 6, 70, 258, 1849], [1, 0, -58, 0, 2209], [1, -8, 118, -424, 2809], [1, 0, 52, 0, 3481], 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-0.08981281520106438, -0.6469011799587931], 'positive_zeros': ['1.04404691290187079653462494449909', '1.96692667827429310912140277982702', '2.36087838488403798550737481117714', '3.05386664618913981513178273339848', '3.69123231822671121566050135027438', '3.93684425527240854475952388210944', '4.62458187822630352965554102488080', '5.18312194044676804963214360655999', '5.54069845675653377448704894206631', '5.93823442298871427005495687259376', '6.39916730847989691864912169611223', '6.85290842552243782297321324218668', '7.26052178614039954076174807420440', '7.928343196908504586934235161855159'], 'prelabel': '4-112e3-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.076465650952455, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1123295267182712918, 'z1': {'__RealLiteral__': 0, 'data': '1.04404691290187079653462494449909', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.96692667827429310912140277982702', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.36087838488403798550737481117714', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 89.57942739416335, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 1404928, 'conductor_radical': 14, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 1, 0, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 2, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 1, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 12, 0, 0, 0, 12, 0, 0, 0, 0, 0, 2, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0], 'euler11': [1, -2, 22, -22, 121], 'euler13': [1, 0, -14, 0, 169], 'euler17': [1, 0, 10, 0, 289], 'euler19': [1, 0, 28, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 6, 54, 138, 529], 'euler29': [1, 6, 66, 174, 841], 'euler3': [1, 0, 4, 0, 9], 'euler31': [1, 0, 18, 0, 961], 'euler37': [1, -2, 26, -74, 1369], 'euler41': [1, 0, 34, 0, 1681], 'euler43': [1, 6, 70, 258, 1849], 'euler47': [1, 0, -58, 0, 2209], 'euler5': [1, 0, -2, 0, 25], 'euler53': [1, -8, 118, -424, 2809], 'euler59': [1, 0, 52, 0, 3481], 'euler61': [1, 0, -34, 0, 3721], 'euler67': [1, -12, 166, -804, 4489], 'euler7': [1, -1, 0, 0, 0], 'euler71': [1, -12, 142, -852, 5041], 'euler73': [1, 0, -106, 0, 5329], 'euler79': [1, 0, 94, 0, 6241], 'euler83': [1, 0, 44, 0, 6889], 'euler89': [1, 0, 30, 0, 7921], 'euler97': [1, 0, 58, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 4, 0, 9], [1, 0, -2, 0, 25], [1, -1, 0, 0, 0], [1, -2, 22, -22, 121], [1, 0, -14, 0, 169], [1, 0, 10, 0, 289], [1, 0, 28, 0, 361], [1, 6, 54, 138, 529], [1, 6, 66, 174, 841], [1, 0, 18, 0, 961], [1, -2, 26, -74, 1369], [1, 0, 34, 0, 1681], [1, 6, 70, 258, 1849], [1, 0, -58, 0, 2209], [1, -8, 118, -424, 2809], [1, 0, 52, 0, 3481], [1, 0, -34, 0, 3721], [1, -12, 166, -804, 4489], [1, -12, 142, -852, 5041], [1, 0, -106, 0, 5329], [1, 0, 94, 0, 6241], [1, 0, 44, 0, 6889], [1, 0, 30, 0, 7921], [1, 0, 58, 0, 9409]], 'index': 25, 'instance_types': ['BMF', 'ECNF', 'BMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.6/h', 'EllipticCurve/2.0.7.1/28672.6/h', 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.8/h', 'EllipticCurve/2.0.7.1/28672.8/h'], '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': '4-112e3-1.1-c1e2-0-25', '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': '4-112e3-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.076465650952455, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1123295267182712918, 'z1': {'__RealLiteral__': 0, 'data': '1.04404691290187079653462494449909', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9621064
{'Lhash': '1323486695806486458415669823543', 'Lhash_array': ['1323486695806486458415669823543'], 'label': '4-112e3-1.1-c1e2-0-25', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/28672.8/h'}
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id: 9620933
{'Lhash': '1323486695806486458415669823543', 'Lhash_array': ['1323486695806486458415669823543'], 'label': '4-112e3-1.1-c1e2-0-25', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.8/h'}
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id: 9620063
{'Lhash': '1323486695806486458415669823543', 'Lhash_array': ['1323486695806486458415669823543'], 'label': '4-112e3-1.1-c1e2-0-25', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/28672.6/h'}
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id: 9619854
{'Lhash': '1323486695806486458415669823543', 'Lhash_array': ['1323486695806486458415669823543'], 'label': '4-112e3-1.1-c1e2-0-25', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.6/h'}