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lfunc_lfunctions • Show schema
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{'Lhash': '334114450005220708506493188005,2548844458067223098831735924779', 'a10': 24, 'a2': -2, 'a3': -2, 'a4': 0, 'a5': -12, 'a6': 4, 'a7': 0, 'a8': 8, 'a9': 27, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 33.43368859106227, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2, 4]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '98.1', 'coefficient_field': '1.1.1.1', 'conductor': 9604, 'conductor_radical': 14, 'degree': 4, 'euler_factors': [[1, 2, 4], [1, 2, -23, 54, 729], [1, 12, 19, 1500, 15625], [1], [1, 48, 973, 63888, 1771561], [1, 112, 7530, 246064, 4826809], [1, 114, 8083, 560082, 24137569], [1, -2, -6855, -13718, 47045881], [1, -120, 2233, -1460040, 148035889], [1, 108, 51694, 2634012, 594823321], [1, -236, 25905, -7030676, 887503681], [1, 146, -29337, 7395338, 2565726409], [1, 252, 153718, 17368092, 4750104241], [1, 752, 300390, 59789264, 6321363049], [1, 12, -103679, 1245876, 10779215329], [1, 174, 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'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.26356982747853890064697396602', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.01068374645846887997242350460', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.01448533349171404466831915028', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 33.43368859106227, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 9604, 'conductor_radical': 14, 'degree': 4, 'dirichlet_coefficients': [1, -2, -2, 0, -12, 4, 0, 8, 27, 24, -48, 0, -112, 0, 24, -16, -114, -54, 2, 0, 0, 96, 120, -16, 125, 224, -154, 0, -108, -48, 236, 0, 96, 228, 0, 0, -146, -4, 224, -96, -252, 0, -752, 0, -324, -240, -12, 32, 0, -250, 228, 0, -174, 308, 576, 0, -4, 216, 138, 0, 380, -472, 0, 64, 1344, -192, 484, 0, -240, 0, 1152, 216, -1150, 292, -250, 0, 0, -448, -776, 192, 308, 504, -756, 0, 1368, 1504, 216, -384, -390, 648, 0, 0, -472, 24, -24, 0, 2660, 0, -1296, 0], 'euler11': [1, 48, 973, 63888, 1771561], 'euler13': [1, 112, 7530, 246064, 4826809], 'euler17': [1, 114, 8083, 560082, 24137569], 'euler19': [1, -2, -6855, -13718, 47045881], 'euler2': [1, 2, 4, 0, 0], 'euler23': [1, -120, 2233, -1460040, 148035889], 'euler29': [1, 108, 51694, 2634012, 594823321], 'euler3': [1, 2, -23, 54, 729], 'euler31': [1, -236, 25905, -7030676, 887503681], 'euler37': [1, 146, -29337, 7395338, 2565726409], 'euler41': [1, 252, 153718, 17368092, 4750104241], 'euler43': [1, 752, 300390, 59789264, 6321363049], 'euler47': [1, 12, -103679, 1245876, 10779215329], 'euler5': [1, 12, 19, 1500, 15625], 'euler53': [1, 174, -118601, 25904598, 22164361129], 'euler59': [1, -138, -186335, -28342302, 42180533641], 'euler61': [1, -380, -82581, -86252780, 51520374361], 'euler67': [1, -484, -66507, -145569292, 90458382169], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, -1152, 1047598, -412313472, 128100283921], 'euler73': [1, 1150, 933483, 447369550, 151334226289], 'euler79': [1, 776, 109137, 382598264, 243087455521], 'euler83': [1, 756, 1286458, 432270972, 326940373369], 'euler89': [1, 390, -552869, 274937910, 496981290961], 'euler97': [1, -2660, 3594246, -2427710180, 832972004929], 'euler_factors': [[1, 2, 4, 0, 0], [1, 2, -23, 54, 729], [1, 12, 19, 1500, 15625], [1, 0, 0, 0, 0], [1, 48, 973, 63888, 1771561], [1, 112, 7530, 246064, 4826809], [1, 114, 8083, 560082, 24137569], [1, -2, -6855, -13718, 47045881], [1, -120, 2233, -1460040, 148035889], [1, 108, 51694, 2634012, 594823321], [1, -236, 25905, -7030676, 887503681], [1, 146, -29337, 7395338, 2565726409], [1, 252, 153718, 17368092, 4750104241], [1, 752, 300390, 59789264, 6321363049], [1, 12, -103679, 1245876, 10779215329], [1, 174, -118601, 25904598, 22164361129], [1, -138, -186335, -28342302, 42180533641], [1, -380, -82581, -86252780, 51520374361], [1, -484, -66507, -145569292, 90458382169], [1, -1152, 1047598, -412313472, 128100283921], [1, 1150, 933483, 447369550, 151334226289], [1, 776, 109137, 382598264, 243087455521], [1, 756, 1286458, 432270972, 326940373369], [1, 390, -552869, 274937910, 496981290961], [1, -2660, 3594246, -2427710180, 832972004929]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/98/4/c/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': '4-98e2-1.1-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': '4-98e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.4046178866012333, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1791062409832661409, 'z1': {'__RealLiteral__': 0, 'data': '0.26356982747853890064697396602', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '334114450005220708506493188005,2548844458067223098831735924779', 'Lhash_array': ['334114450005220708506493188005', '2548844458067223098831735924779'], 'label': '4-98e2-1.1-c3e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/98/4/c/b'}