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lfunc_lfunctions • Show schema
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{'Lhash': '1183092412529211039129781262190', 'a10': -125, 'a2': -5, 'a3': 0, 'a4': -7, 'a5': 25, 'a6': 0, 'a7': -244, 'a8': 195, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 93.82453459059369, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, -25]], [13, [1, 169]]], 'bad_primes': [3, 5, 13], 'central_character': '585.1', 'coefficient_field': '1.1.1.1', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'euler_factors': [[1, 5, 32], [1], [1, -25], [1, 244, 16807], [1, 794, 161051], [1, 169], [1, -1534, 1419857], [1, -2706, 2476099], [1, -702, 6436343], [1, -5038, 20511149], [1, 3634, 28629151], [1, 7058, 69343957], [1, -294, 115856201], [1, -7618, 147008443], [1, -3020, 229345007], [1, 626, 418195493], [1, -30066, 714924299], [1, 5806, 844596301], [1, 12436, 1350125107], [1, 4734, 1804229351], [1, 14694, 2073071593], [1, 39804, 3077056399], [1, -41776, 3939040643], [1, 7970, 5584059449], [1, 78050, 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'7.68950830140404416187585011146193', '8.789863080363405286551356528908270', '9.743902646471741272122261448815119'], 'prelabel': '2-585-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.686306550517266, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'trace_hash': 901969207801863955, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.933295351507904149325908147535', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.63877058162349065955732485083', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.42043726312884599581113219166', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 93.82453459059369, 'bad_primes': [3, 5, 13], 'central_character': '1.1', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'dirichlet_coefficients': [1, -5, 0, -7, 25, 0, -244, 195, 0, -125, -794, 0, -169, 1220, 0, -751, 1534, 0, 2706, -175, 0, 3970, 702, 0, 625, 845, 0, 1708, 5038, 0, -3634, -2485, 0, -7670, -6100, 0, -7058, -13530, 0, 4875, 294, 0, 7618, 5558, 0, -3510, 3020, 0, 42729, -3125, 0, 1183, -626, 0, -19850, -47580, 0, -25190, 30066, 0, -5806, 18170, 0, 36457, -4225, 0, -12436, -10738, 0, 30500, -4734, 0, -14694, 35290, 0, -18942, 193736, 0, -39804, -18775, 0, -1470, 41776, 0, 38350, -38090, 0, -154830, -7970, 0, 41236, -4914, 0, -15100, 67650, 0, -78050, -213645, 0, -4375], 'euler11': [1, 794, 161051], 'euler13': [1, 169, 0], 'euler17': [1, -1534, 1419857], 'euler19': [1, -2706, 2476099], 'euler2': [1, 5, 32], 'euler23': [1, -702, 6436343], 'euler29': [1, -5038, 20511149], 'euler3': [1, 0, 0], 'euler31': [1, 3634, 28629151], 'euler37': [1, 7058, 69343957], 'euler41': [1, -294, 115856201], 'euler43': [1, -7618, 147008443], 'euler47': [1, -3020, 229345007], 'euler5': [1, -25, 0], 'euler53': [1, 626, 418195493], 'euler59': [1, -30066, 714924299], 'euler61': [1, 5806, 844596301], 'euler67': [1, 12436, 1350125107], 'euler7': [1, 244, 16807], 'euler71': [1, 4734, 1804229351], 'euler73': [1, 14694, 2073071593], 'euler79': [1, 39804, 3077056399], 'euler83': [1, -41776, 3939040643], 'euler89': [1, 7970, 5584059449], 'euler97': [1, 78050, 8587340257], 'euler_factors': [[1, 5, 32], [1, 0, 0], [1, -25, 0], [1, 244, 16807], [1, 794, 161051], [1, 169, 0], [1, -1534, 1419857], [1, -2706, 2476099], [1, -702, 6436343], [1, -5038, 20511149], [1, 3634, 28629151], [1, 7058, 69343957], [1, -294, 115856201], [1, -7618, 147008443], [1, -3020, 229345007], [1, 626, 418195493], [1, -30066, 714924299], [1, 5806, 844596301], [1, 12436, 1350125107], [1, 4734, 1804229351], [1, 14694, 2073071593], [1, 39804, 3077056399], [1, -41776, 3939040643], [1, 7970, 5584059449], [1, 78050, 8587340257]], 'index': 45, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/6/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/585/6/a/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': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-585-1.1-c5-0-45', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-585-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.686306550517266, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'trace_hash': 901969207801863955, 'z1': {'__RealLiteral__': 0, 'data': '0.933295351507904149325908147535', 'prec': 107}}
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lfunc_instances • Show schema
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id: 20853203
{'Lhash': '1183092412529211039129781262190', 'Lhash_array': ['1183092412529211039129781262190'], 'label': '2-585-1.1-c5-0-45', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/6/a/a'}
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id: 24591730
{'Lhash': '1183092412529211039129781262190', 'Lhash_array': ['1183092412529211039129781262190'], 'label': '2-585-1.1-c5-0-45', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/6/a/a/1/1'}