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lfunc_lfunctions • Show schema
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{'Lhash': '1610141255272650421999073261676', 'a10': 84, 'a2': 4, 'a3': 0, 'a4': 16, 'a5': 21, 'a6': 0, 'a7': 74, 'a8': 64, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.98217880970287, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -4]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '162.1', 'coefficient_field': '1.1.1.1', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[1, -4], [1], [1, -21, 3125], [1, -74, 16807], [1, -270, 161051], [1, 115, 371293], [1, 861, 1419857], [1, -1850, 2476099], [1, -3618, 6436343], [1, -1125, 20511149], [1, -5228, 28629151], [1, -9917, 69343957], [1, -10758, 115856201], [1, 19714, 147008443], [1, -9984, 229345007], [1, -36726, 418195493], [1, -26460, 714924299], [1, 53779, 844596301], [1, 12934, 1350125107], [1, 4254, 1804229351], [1, 17521, 2073071593], [1, 36946, 3077056399], [1, 76416, 3939040643], [1, 45357, 5584059449], [1, -127574, 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'7.58855218103548343461047267106415', '8.925599390208910191938525609956907', '10.02002315784318190620953317007565', '11.28350220388998770695686811361629', '11.86939120401867914331251600868632'], 'prelabel': '2-162-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.097271702558426, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'trace_hash': 1665341640732003788, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.27017748816807925944253622820', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.75100931142022291058618139198', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.25849581621773065977264689695', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.98217880970287, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'dirichlet_coefficients': [1, 4, 0, 16, 21, 0, 74, 64, 0, 84, 270, 0, -115, 296, 0, 256, -861, 0, 1850, 336, 0, 1080, 3618, 0, -2684, -460, 0, 1184, 1125, 0, 5228, 1024, 0, -3444, 1554, 0, 9917, 7400, 0, 1344, 10758, 0, -19714, 4320, 0, 14472, 9984, 0, -11331, -10736, 0, -1840, 36726, 0, 5670, 4736, 0, 4500, 26460, 0, -53779, 20912, 0, 4096, -2415, 0, -12934, -13776, 0, 6216, -4254, 0, -17521, 39668, 0, 29600, 19980, 0, -36946, 5376, 0, 43032, -76416, 0, -18081, -78856, 0, 17280, -45357, 0, -8510, 57888, 0, 39936, 38850, 0, 127574, -45324, 0, -42944], 'euler11': [1, -270, 161051], 'euler13': [1, 115, 371293], 'euler17': [1, 861, 1419857], 'euler19': [1, -1850, 2476099], 'euler2': [1, -4, 0], 'euler23': [1, -3618, 6436343], 'euler29': [1, -1125, 20511149], 'euler3': [1, 0, 0], 'euler31': [1, -5228, 28629151], 'euler37': [1, -9917, 69343957], 'euler41': [1, -10758, 115856201], 'euler43': [1, 19714, 147008443], 'euler47': [1, -9984, 229345007], 'euler5': [1, -21, 3125], 'euler53': [1, -36726, 418195493], 'euler59': [1, -26460, 714924299], 'euler61': [1, 53779, 844596301], 'euler67': [1, 12934, 1350125107], 'euler7': [1, -74, 16807], 'euler71': [1, 4254, 1804229351], 'euler73': [1, 17521, 2073071593], 'euler79': [1, 36946, 3077056399], 'euler83': [1, 76416, 3939040643], 'euler89': [1, 45357, 5584059449], 'euler97': [1, -127574, 8587340257], 'euler_factors': [[1, -4, 0], [1, 0, 0], [1, -21, 3125], [1, -74, 16807], [1, -270, 161051], [1, 115, 371293], [1, 861, 1419857], [1, -1850, 2476099], [1, -3618, 6436343], [1, -1125, 20511149], [1, -5228, 28629151], [1, -9917, 69343957], [1, -10758, 115856201], [1, 19714, 147008443], [1, -9984, 229345007], [1, -36726, 418195493], [1, -26460, 714924299], [1, 53779, 844596301], [1, 12934, 1350125107], [1, 4254, 1804229351], [1, 17521, 2073071593], [1, 36946, 3077056399], [1, 76416, 3939040643], [1, 45357, 5584059449], [1, -127574, 8587340257]], 'index': 8, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/6/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/162/6/a/b'], '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': '2-162-1.1-c5-0-8', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-162-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.097271702558426, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'trace_hash': 1665341640732003788, 'z1': {'__RealLiteral__': 0, 'data': '1.27017748816807925944253622820', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20627472
{'Lhash': '1610141255272650421999073261676', 'Lhash_array': ['1610141255272650421999073261676'], 'label': '2-162-1.1-c5-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/6/a/b'}
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id: 24560749
{'Lhash': '1610141255272650421999073261676', 'Lhash_array': ['1610141255272650421999073261676'], 'label': '2-162-1.1-c5-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/6/a/b/1/1'}