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lfunc_lfunctions • Show schema
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{'Lhash': '4053241745938740214059524214866,5285207810825826064041359320641', 'a10': 8, 'a2': -2, 'a3': -4, 'a4': 2, 'a5': -4, 'a6': 8, 'a7': -6, 'a8': 0, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.40806954898944675, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2, 2]], [5, [1, 4, 5]]], 'bad_primes': [2, 5], 'central_character': '80.1', 'coefficient_field': '1.1.1.1', 'conductor': 6400, 'conductor_radical': 10, 'degree': 4, 'euler_factors': [[1, 2, 2], [1, 4, 10, 12, 9], [1, 4, 5], [1, 6, 18, 42, 49], [1, 2, 2, 22, 121], [1, 0, -22, 0, 169], [1, -2, 2, -34, 289], [1, 6, 18, 114, 361], [1, 2, 2, 46, 529], [1, 14, 98, 406, 841], [1, 0, -58, 0, 961], [1, 0, -38, 0, 1369], [1, 0, -66, 0, 1681], [1, 0, -70, 0, 1849], [1, 14, 98, 658, 2209], [1, 16, 170, 848, 2809], [1, -6, 18, -354, 3481], [1, 2, 2, 122, 3721], [1, 0, -118, 0, 4489], [1, 0, 142, 0, 5041], [1, -6, 18, -438, 5329], [1, -16, 222, -1264, 6241], [1, 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'14.21442938078161757019809759423740'], 'prelabel': '4-80e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.799251660098522, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 299600904686788309, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.19744395278082895586299779894', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.16929381792922326649904005931', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.18013618333723223342449259876', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 0.40806954898944675, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 6400, 'conductor_radical': 10, 'degree': 4, 'dirichlet_coefficients': [1, -2, -4, 2, -4, 8, -6, 0, 6, 8, -2, -8, 0, 12, 16, -4, 2, -12, -6, -8, 24, 4, -2, 0, 11, 0, 4, -12, -14, -32, 0, 8, 8, -4, 24, 12, 0, 12, 0, 0, 0, -48, 0, -4, -24, 4, -14, 16, 18, -22, -8, 0, -16, -8, 8, 0, 24, 28, 6, 32, -2, 0, -36, -8, 0, -16, 0, 4, 8, -48, 0, 0, 6, 0, -44, -12, 12, 0, 16, 16, -37, 0, -4, 48, -8, 0, 56, 0, -12, 48, 0, -4, 0, 28, 24, -32, -22, -36, -12, 22], 'euler11': [1, 2, 2, 22, 121], 'euler13': [1, 0, -22, 0, 169], 'euler17': [1, -2, 2, -34, 289], 'euler19': [1, 6, 18, 114, 361], 'euler2': [1, 2, 2, 0, 0], 'euler23': [1, 2, 2, 46, 529], 'euler29': [1, 14, 98, 406, 841], 'euler3': [1, 4, 10, 12, 9], 'euler31': [1, 0, -58, 0, 961], 'euler37': [1, 0, -38, 0, 1369], 'euler41': [1, 0, -66, 0, 1681], 'euler43': [1, 0, -70, 0, 1849], 'euler47': [1, 14, 98, 658, 2209], 'euler5': [1, 4, 5, 0, 0], 'euler53': [1, 16, 170, 848, 2809], 'euler59': [1, -6, 18, -354, 3481], 'euler61': [1, 2, 2, 122, 3721], 'euler67': [1, 0, -118, 0, 4489], 'euler7': [1, 6, 18, 42, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, -6, 18, -438, 5329], 'euler79': [1, -16, 222, -1264, 6241], 'euler83': [1, 4, 170, 332, 6889], 'euler89': [1, 12, 214, 1068, 7921], 'euler97': [1, 22, 242, 2134, 9409], 'euler_factors': [[1, 2, 2, 0, 0], [1, 4, 10, 12, 9], [1, 4, 5, 0, 0], [1, 6, 18, 42, 49], [1, 2, 2, 22, 121], [1, 0, -22, 0, 169], [1, -2, 2, -34, 289], [1, 6, 18, 114, 361], [1, 2, 2, 46, 529], [1, 14, 98, 406, 841], [1, 0, -58, 0, 961], [1, 0, -38, 0, 1369], [1, 0, -66, 0, 1681], [1, 0, -70, 0, 1849], [1, 14, 98, 658, 2209], [1, 16, 170, 848, 2809], [1, -6, 18, -354, 3481], [1, 2, 2, 122, 3721], [1, 0, -118, 0, 4489], [1, 0, 142, 0, 5041], [1, -6, 18, -438, 5329], [1, -16, 222, -1264, 6241], [1, 4, 170, 332, 6889], [1, 12, 214, 1068, 7921], [1, 22, 242, 2134, 9409]], 'index': 15, 'instance_types': ['G2Q', 'CMF'], 'instance_urls': ['Genus2Curve/Q/6400/f', 'ModularForm/GL2/Q/holomorphic/80/2/s/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': True, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-80e2-1.1-c1e2-0-15', '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': 2, 'prelabel': '4-80e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.799251660098522, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 299600904686788309, 'z1': {'__RealLiteral__': 0, 'data': '3.19744395278082895586299779894', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9960114
{'Lhash': '4053241745938740214059524214866,5285207810825826064041359320641', 'Lhash_array': ['4053241745938740214059524214866', '5285207810825826064041359320641'], 'label': '4-80e2-1.1-c1e2-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/80/2/s/a'}
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id: 1223435
{'Lhash': '299600904686788309', 'Lhash_array': ['299600904686788309'], 'label': '4-80e2-1.1-c1e2-0-15', 'type': 'G2Q', 'url': 'Genus2Curve/Q/6400/f'}