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lfunc_lfunctions • Show schema
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{'Lhash': '1789850358040983091566404083884,3735296310576855549188236941193', 'a10': -16, 'a2': 1, 'a3': 2, 'a4': 8, 'a5': -16, 'a6': 2, 'a7': 0, 'a8': 23, 'a9': 27, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.358422147765568, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[7, [1]]], 'bad_primes': [7], 'central_character': '49.1', 'coefficient_field': '1.1.1.1', 'conductor': 2401, 'conductor_radical': 7, 'degree': 4, 'euler_factors': [[1, -1, -7, -8, 64], [1, -2, -23, -54, 729], [1, 16, 131, 2000, 15625], [1], [1, -8, -1267, -10648, 1771561], [1, -56, 5178, -123032, 4826809], [1, 54, -1997, 265302, 24137569], [1, -110, 5241, -754490, 47045881], [1, 48, -9863, 584016, 148035889], [1, 220, 60878, 5365580, 594823321], [1, 12, -29647, 357492, 887503681], [1, -246, 9863, -12460638, 2565726409], [1, -364, 170966, -25087244, 4750104241], [1, -256, 175398, -20353792, 6321363049], [1, 324, 1153, 33638652, 10779215329], [1, -162, 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{'algebraic': True, 'analytic_conductor': 8.358422147765568, 'bad_primes': [7], 'central_character': '1.1', 'conductor': 2401, 'conductor_radical': 7, 'degree': 4, 'dirichlet_coefficients': [1, 1, 2, 8, -16, 2, 0, 23, 27, -16, 8, 16, 56, 0, -32, 23, -54, 27, 110, -128, 0, 8, -48, 46, 125, 56, 154, 0, -220, -32, -12, 184, 16, -54, 0, 216, 246, 110, 112, -368, 364, 0, 256, 64, -432, -48, -324, 46, 0, 125, -108, 448, 162, 154, -128, 0, 220, -220, -810, -256, 488, -12, 0, 17, -896, 16, -244, -432, -96, 0, -1536, 621, 702, 246, 250, 880, 0, 112, -440, -368, 308, 364, -2604, 0, 864, 256, -440, 184, -730, -432, 0, -384, -24, -324, -1760, 368, 588, 0, 216, 1000], 'euler11': [1, -8, -1267, -10648, 1771561], 'euler13': [1, -56, 5178, -123032, 4826809], 'euler17': [1, 54, -1997, 265302, 24137569], 'euler19': [1, -110, 5241, -754490, 47045881], 'euler2': [1, -1, -7, -8, 64], 'euler23': [1, 48, -9863, 584016, 148035889], 'euler29': [1, 220, 60878, 5365580, 594823321], 'euler3': [1, -2, -23, -54, 729], 'euler31': [1, 12, -29647, 357492, 887503681], 'euler37': [1, -246, 9863, -12460638, 2565726409], 'euler41': [1, -364, 170966, -25087244, 4750104241], 'euler43': [1, -256, 175398, -20353792, 6321363049], 'euler47': [1, 324, 1153, 33638652, 10779215329], 'euler5': [1, 16, 131, 2000, 15625], 'euler53': [1, -162, -122633, -24118074, 22164361129], 'euler59': [1, 810, 450721, 166356990, 42180533641], 'euler61': [1, -488, 11163, -110766728, 51520374361], 'euler67': [1, 244, -241227, 73386172, 90458382169], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 1536, 1305646, 549751296, 128100283921], 'euler73': [1, -702, 103787, -273089934, 151334226289], 'euler79': [1, 440, -299439, 216937160, 243087455521], 'euler83': [1, 2604, 2838778, 1488933348, 326940373369], 'euler89': [1, 730, -172069, 514627370, 496981290961], 'euler97': [1, -588, 1911782, -536651724, 832972004929], 'euler_factors': [[1, -1, -7, -8, 64], [1, -2, -23, -54, 729], [1, 16, 131, 2000, 15625], [1, 0, 0, 0, 0], [1, -8, -1267, -10648, 1771561], [1, -56, 5178, -123032, 4826809], [1, 54, -1997, 265302, 24137569], [1, -110, 5241, -754490, 47045881], [1, 48, -9863, 584016, 148035889], [1, 220, 60878, 5365580, 594823321], [1, 12, -29647, 357492, 887503681], [1, -246, 9863, -12460638, 2565726409], [1, -364, 170966, -25087244, 4750104241], [1, -256, 175398, -20353792, 6321363049], [1, 324, 1153, 33638652, 10779215329], [1, -162, -122633, -24118074, 22164361129], [1, 810, 450721, 166356990, 42180533641], [1, -488, 11163, -110766728, 51520374361], [1, 244, -241227, 73386172, 90458382169], [1, 1536, 1305646, 549751296, 128100283921], [1, -702, 103787, -273089934, 151334226289], [1, 440, -299439, 216937160, 243087455521], [1, 2604, 2838778, 1488933348, 326940373369], [1, 730, -172069, 514627370, 496981290961], [1, -588, 1911782, -536651724, 832972004929]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/49/4/c/c'], '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': '4-7e4-1.1-c3e2-0-0', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 0, 'prelabel': '4-7e4-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.700321613778197, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1356045812664012321, 'z1': {'__RealLiteral__': 0, 'data': '1.41194297365436200775023785024', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1789850358040983091566404083884,3735296310576855549188236941193', 'Lhash_array': ['1789850358040983091566404083884', '3735296310576855549188236941193'], 'factors': ['2-7e2-7.2-c3-0-1', '2-7e2-7.4-c3-0-5'], 'label': '4-7e4-1.1-c3e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/49/4/c/c'}