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lfunc_lfunctions • Show schema
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{'Lhash': '357934914648268455245907814290,911603465570934530010028446987', 'a10': -40, 'a2': -4, 'a3': -6, 'a4': 12, 'a5': 10, 'a6': 24, 'a7': 0, 'a8': -32, 'a9': 27, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7522.5799329890115, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 4, 4]], [3, [1, 6, 9]], [5, [1, -10, 25]], [7, [1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1470.1', 'coefficient_field': '1.1.1.1', 'conductor': 2160900, 'conductor_radical': 210, 'degree': 4, 'euler_factors': [[1, 4, 4], [1, 6, 9], [1, -10, 25], [1], [1, 58, 2998, 77198, 1771561], [1, 56, 3158, 123032, 4826809], [1, -10, -2774, -49130, 24137569], [1, -2, 1094, -13718, 47045881], [1, 130, 15934, 1581710, 148035889], [1, 34, -12038, 829226, 594823321], [1, 344, 70986, 10248104, 887503681], [1, 54, -43910, 2735262, 2565726409], [1, 60, 130662, 4135260, 4750104241], [1, 206, 84278, 16378442, 6321363049], [1, -958, 432542, -99462434, 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'data': '0.71912833505289888278488148277', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.60824305236788146370921990300', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 7522.5799329890115, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 2160900, 'conductor_radical': 210, 'degree': 4, 'dirichlet_coefficients': [1, -4, -6, 12, 10, 24, 0, -32, 27, -40, -58, -72, -56, 0, -60, 80, 10, -108, 2, 120, 0, 232, -130, 192, 75, 224, -108, 0, -34, 240, -344, -192, 348, -40, 0, 324, -54, -8, 336, -320, -60, 0, -206, -696, 270, 520, 958, -480, 0, -300, -60, -672, 1350, 432, -580, 0, -12, 136, 132, -720, -18, 1376, 0, 448, -560, -1392, 1486, 120, 780, 0, -1364, -864, 44, 216, -450, 24, 0, -1344, -304, 800, 405, 240, -1892, 0, 100, 824, 204, 1856, -596, -1080, 0, -1560, 2064, -3832, 20, 1152, -508, 0, -1566, 900], 'euler11': [1, 58, 2998, 77198, 1771561], 'euler13': [1, 56, 3158, 123032, 4826809], 'euler17': [1, -10, -2774, -49130, 24137569], 'euler19': [1, -2, 1094, -13718, 47045881], 'euler2': [1, 4, 4, 0, 0], 'euler23': [1, 130, 15934, 1581710, 148035889], 'euler29': [1, 34, -12038, 829226, 594823321], 'euler3': [1, 6, 9, 0, 0], 'euler31': [1, 344, 70986, 10248104, 887503681], 'euler37': [1, 54, -43910, 2735262, 2565726409], 'euler41': [1, 60, 130662, 4135260, 4750104241], 'euler43': [1, 206, 84278, 16378442, 6321363049], 'euler47': [1, -958, 432542, -99462434, 10779215329], 'euler5': [1, -10, 25, 0, 0], 'euler53': [1, -1350, 752874, -200983950, 22164361129], 'euler59': [1, -132, 364614, -27110028, 42180533641], 'euler61': [1, 18, 392938, 4085658, 51520374361], 'euler67': [1, -1486, 1149030, -446933818, 90458382169], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 1364, 1130446, 488190604, 128100283921], 'euler73': [1, -44, 382598, -17116748, 151334226289], 'euler79': [1, 304, 1009182, 149883856, 243087455521], 'euler83': [1, 1892, 2020310, 1081821004, 326940373369], 'euler89': [1, 596, 1369462, 420161524, 496981290961], 'euler97': [1, 508, 524342, 463637884, 832972004929], 'euler_factors': [[1, 4, 4, 0, 0], [1, 6, 9, 0, 0], [1, -10, 25, 0, 0], [1, 0, 0, 0, 0], [1, 58, 2998, 77198, 1771561], [1, 56, 3158, 123032, 4826809], [1, -10, -2774, -49130, 24137569], [1, -2, 1094, -13718, 47045881], [1, 130, 15934, 1581710, 148035889], [1, 34, -12038, 829226, 594823321], [1, 344, 70986, 10248104, 887503681], [1, 54, -43910, 2735262, 2565726409], [1, 60, 130662, 4135260, 4750104241], [1, 206, 84278, 16378442, 6321363049], [1, -958, 432542, -99462434, 10779215329], [1, -1350, 752874, -200983950, 22164361129], [1, -132, 364614, -27110028, 42180533641], [1, 18, 392938, 4085658, 51520374361], [1, -1486, 1149030, -446933818, 90458382169], [1, 1364, 1130446, 488190604, 128100283921], [1, -44, 382598, -17116748, 151334226289], [1, 304, 1009182, 149883856, 243087455521], [1, 1892, 2020310, 1081821004, 326940373369], [1, 596, 1369462, 420161524, 496981290961], [1, 508, 524342, 463637884, 832972004929]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1470/4/a/bf'], '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': '4-1470e2-1.1-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': '4-1470e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 9.313045028799053, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 157166397403211507, 'z1': {'__RealLiteral__': 0, 'data': '0.28236086077963865199454561622', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '357934914648268455245907814290,911603465570934530010028446987', 'Lhash_array': ['357934914648268455245907814290', '911603465570934530010028446987'], 'label': '4-1470e2-1.1-c3e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1470/4/a/bf'}