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lfunc_lfunctions • Show schema
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{'Lhash': '537967466765278873422552412433,2117234900734205554536409595311', 'a10': 18, 'a2': 2, 'a3': 0, 'a4': 0, 'a5': 9, 'a6': 0, 'a7': 0, 'a8': -8, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2708.128775876044, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 4]], [3, [1]], [7, [1]]], 'bad_primes': [2, 3, 7], 'central_character': '882.1', 'coefficient_field': '1.1.1.1', 'conductor': 777924, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1, -2, 4], [1], [1, -9, -44, -1125, 15625], [1], [1, 57, 1918, 75867, 1771561], [1, -140, 9294, -307580, 4826809], [1, 51, -2312, 250563, 24137569], [1, -5, -6834, -34295, 47045881], [1, -69, -7406, -839523, 148035889], [1, 228, 61774, 5560692, 594823321], [1, -23, -29262, -685193, 887503681], [1, -253, 13356, -12815209, 2565726409], [1, 84, 139606, 5789364, 4750104241], [1, 248, 174390, 19717736, 6321363049], [1, 201, -63422, 20868423, 10779215329], [1, 393, 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{'algebraic': True, 'analytic_conductor': 2708.128775876044, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 777924, 'conductor_radical': 42, 'degree': 4, 'dirichlet_coefficients': [1, 2, 0, 0, 9, 0, 0, -8, 0, 18, -57, 0, 140, 0, 0, -16, -51, 0, 5, 0, 0, -114, 69, 0, 125, 280, 0, 0, -228, 0, 23, 0, 0, -102, 0, 0, 253, 10, 0, -72, -84, 0, -248, 0, 0, 138, -201, 0, 0, 250, 0, 0, -393, 0, -513, 0, 0, -456, -219, 0, -709, 46, 0, 64, 1260, 0, -419, 0, 0, 0, 192, 0, -313, 506, 0, 0, 0, 0, -461, -144, 0, -168, -1176, 0, -459, -496, 0, 456, 1017, 0, 0, 0, 0, -402, 45, 0, 3668, 0, 0, 0], 'euler11': [1, 57, 1918, 75867, 1771561], 'euler13': [1, -140, 9294, -307580, 4826809], 'euler17': [1, 51, -2312, 250563, 24137569], 'euler19': [1, -5, -6834, -34295, 47045881], 'euler2': [1, -2, 4, 0, 0], 'euler23': [1, -69, -7406, -839523, 148035889], 'euler29': [1, 228, 61774, 5560692, 594823321], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -23, -29262, -685193, 887503681], 'euler37': [1, -253, 13356, -12815209, 2565726409], 'euler41': [1, 84, 139606, 5789364, 4750104241], 'euler43': [1, 248, 174390, 19717736, 6321363049], 'euler47': [1, 201, -63422, 20868423, 10779215329], 'euler5': [1, -9, -44, -1125, 15625], 'euler53': [1, 393, 5572, 58508661, 22164361129], 'euler59': [1, 219, -157418, 44978001, 42180533641], 'euler61': [1, 709, 275700, 160929529, 51520374361], 'euler67': [1, 419, -125202, 126019697, 90458382169], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, -192, 725038, -68718912, 128100283921], 'euler73': [1, 313, -291048, 121762321, 151334226289], 'euler79': [1, 461, -280518, 227290979, 243087455521], 'euler83': [1, 1176, 1489318, 672421512, 326940373369], 'euler89': [1, -1017, 329320, -716953473, 496981290961], 'euler97': [1, -3668, 5188902, -3347684564, 832972004929], 'euler_factors': [[1, -2, 4, 0, 0], [1, 0, 0, 0, 0], [1, -9, -44, -1125, 15625], [1, 0, 0, 0, 0], [1, 57, 1918, 75867, 1771561], [1, -140, 9294, -307580, 4826809], [1, 51, -2312, 250563, 24137569], [1, -5, -6834, -34295, 47045881], [1, -69, -7406, -839523, 148035889], [1, 228, 61774, 5560692, 594823321], [1, -23, -29262, -685193, 887503681], [1, -253, 13356, -12815209, 2565726409], [1, 84, 139606, 5789364, 4750104241], [1, 248, 174390, 19717736, 6321363049], [1, 201, -63422, 20868423, 10779215329], [1, 393, 5572, 58508661, 22164361129], [1, 219, -157418, 44978001, 42180533641], [1, 709, 275700, 160929529, 51520374361], [1, 419, -125202, 126019697, 90458382169], [1, -192, 725038, -68718912, 128100283921], [1, 313, -291048, 121762321, 151334226289], [1, 461, -280518, 227290979, 243087455521], [1, 1176, 1489318, 672421512, 326940373369], [1, -1017, 329320, -716953473, 496981290961], [1, -3668, 5188902, -3347684564, 832972004929]], 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/882/4/g/u'], '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': '4-882e2-1.1-c3e2-0-14', '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': '4-882e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.213853659803701, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1489459971669392540, 'z1': {'__RealLiteral__': 0, 'data': '0.42438150281191247574806351189', 'prec': 103}}
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{'Lhash': '537967466765278873422552412433,2117234900734205554536409595311', 'Lhash_array': ['537967466765278873422552412433', '2117234900734205554536409595311'], 'label': '4-882e2-1.1-c3e2-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/882/4/g/u'}