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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 2, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -2, 'Lhash': '615700250989792885,1352987475818396749', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.894427190999916, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 73.65655359259515, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, -2, 1]], [19, [1, 0, -1]]], 'bad_primes': [2, 5, 19], 'central_character': '1155200.1', 'coefficient_field': '1.1.1.1', 'conductor': 1155200, 'conductor_radical': 190, 'degree': 4, 'euler_factors': [[1], [1, 0, 2, 0, 9], [1, -2, 1], [1, 0, -2, 0, 49], [1, 0, 6, 0, 121], [1, 0, 26, 0, 169], [1, -12, 70, -204, 289], [1, 0, -1], [1, 0, -18, 0, 529], [1, 12, 94, 348, 841], [1, 0, -2, 0, 961], [1, 16, 138, 592, 1369], [1, 4, 86, 164, 1681], [1, 0, 86, 0, 1849], [1, 0, -50, 0, 2209], [1, -8, 122, -424, 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-0.9335804778937813, -0.3250197930209975, 0.12802366447917968], 'positive_zeros': ['1.43164889163469816022501322948697', '1.59759174812609501372900700414141', '2.60381772911094501574186169990456', '3.07425032684048770058081362283557', '3.65364713148753234880290069946554', '3.89039366794407092271004025253966', '5.10437002998588623603580405147540', '5.14236160489505260986626044288378', '5.54689473112839455757595566430376', '6.07553649243771927211326383485146', '6.26604533373139617436495529729271', '7.15092239567899718438965748252261', '7.39113364510721793818506063600287', '7.71376887273613652020249641716914'], 'prelabel': '4-1155200-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.929563044885252, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1968687726808189634, 'z1': {'__RealLiteral__': 0, 'data': '1.43164889163469816022501322948697', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.59759174812609501372900700414141', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.60381772911094501574186169990456', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 73.65655359259515, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 1155200, 'conductor_radical': 190, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 24, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, 6, 0, 121], 'euler13': [1, 0, 26, 0, 169], 'euler17': [1, -12, 70, -204, 289], 'euler19': [1, 0, -1, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -18, 0, 529], 'euler29': [1, 12, 94, 348, 841], 'euler3': [1, 0, 2, 0, 9], 'euler31': [1, 0, -2, 0, 961], 'euler37': [1, 16, 138, 592, 1369], 'euler41': [1, 4, 86, 164, 1681], 'euler43': [1, 0, 86, 0, 1849], 'euler47': [1, 0, -50, 0, 2209], 'euler5': [1, -2, 1, 0, 0], 'euler53': [1, -8, 122, -424, 2809], 'euler59': [1, 0, 54, 0, 3481], 'euler61': [1, 28, 318, 1708, 3721], 'euler67': [1, 0, 130, 0, 4489], 'euler7': [1, 0, -2, 0, 49], 'euler71': [1, 0, 78, 0, 5041], 'euler73': [1, 4, 150, 292, 5329], 'euler79': [1, 0, 142, 0, 6241], 'euler83': [1, 0, 22, 0, 6889], 'euler89': [1, -12, 214, -1068, 7921], 'euler97': [1, 0, 194, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 2, 0, 9], [1, -2, 1, 0, 0], [1, 0, -2, 0, 49], [1, 0, 6, 0, 121], [1, 0, 26, 0, 169], [1, -12, 70, -204, 289], [1, 0, -1, 0, 0], [1, 0, -18, 0, 529], [1, 12, 94, 348, 841], [1, 0, -2, 0, 961], [1, 16, 138, 592, 1369], [1, 4, 86, 164, 1681], [1, 0, 86, 0, 1849], [1, 0, -50, 0, 2209], [1, -8, 122, -424, 2809], [1, 0, 54, 0, 3481], [1, 28, 318, 1708, 3721], [1, 0, 130, 0, 4489], [1, 0, 78, 0, 5041], [1, 4, 150, 292, 5329], [1, 0, 142, 0, 6241], [1, 0, 22, 0, 6889], [1, -12, 214, -1068, 7921], [1, 0, 194, 0, 9409]], 'index': 14, 'instance_types': ['BMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/72200.2/c', 'EllipticCurve/2.0.4.1/72200.2/c'], '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': '4-1155200-1.1-c1e2-0-14', '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': '4-1155200-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.929563044885252, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1968687726808189634, 'z1': {'__RealLiteral__': 0, 'data': '1.43164889163469816022501322948697', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9736979
{'Lhash': '615700250989792885,1352987475818396749', 'Lhash_array': ['615700250989792885', '1352987475818396749'], 'label': '4-1155200-1.1-c1e2-0-14', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/72200.2/c'}
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id: 9737079
{'Lhash': '615700250989792885,1352987475818396749', 'Lhash_array': ['615700250989792885', '1352987475818396749'], 'label': '4-1155200-1.1-c1e2-0-14', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/72200.2/c'}