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lfunc_lfunctions • Show schema
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{'Lhash': '869867943412694818632822237243,2551707628207715927103078552094', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 15, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 176.23703508147932, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '225.1', 'coefficient_field': '1.1.1.1', 'conductor': 50625, 'conductor_radical': 15, 'degree': 4, 'euler_factors': [[1, 0, -15, 0, 64], [1], [1], [1, 0, -110, 0, 117649], [1, 104, 5366, 138424, 1771561], [1, 0, -3910, 0, 4826809], [1, 0, -9630, 0, 24137569], [1, -40, 14118, -274360, 47045881], [1, 0, 3890, 0, 148035889], [1, -460, 101678, -11218940, 594823321], [1, 576, 142526, 17159616, 887503681], [1, 0, -100150, 0, 2565726409], [1, 244, 152726, 16816724, 4750104241], [1, 0, -123670, 0, 6321363049], [1, 0, -142110, 0, 10779215329], [1, 0, -183510, 0, 22164361129], [1, -200, 420758, -41075800, 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{'algebraic': True, 'analytic_conductor': 176.23703508147932, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 50625, 'conductor_radical': 15, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 15, 0, 0, 0, 0, 0, 0, -104, 0, 0, 0, 0, 161, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 460, 0, -576, 0, 0, 0, 0, 0, 0, 0, 0, 0, -244, 0, 0, -1560, 0, 0, 0, 0, 110, 0, 0, 0, 0, 0, 0, 0, 0, 0, 200, 0, 1484, 0, 0, 1455, 0, 0, 0, 0, 0, 0, 656, 0, 0, 0, 0, 600, 0, 0, 480, 0, 0, 0, 0, 0, 0, 0, 0, 0, 660, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 104, 5366, 138424, 1771561], 'euler13': [1, 0, -3910, 0, 4826809], 'euler17': [1, 0, -9630, 0, 24137569], 'euler19': [1, -40, 14118, -274360, 47045881], 'euler2': [1, 0, -15, 0, 64], 'euler23': [1, 0, 3890, 0, 148035889], 'euler29': [1, -460, 101678, -11218940, 594823321], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 576, 142526, 17159616, 887503681], 'euler37': [1, 0, -100150, 0, 2565726409], 'euler41': [1, 244, 152726, 16816724, 4750104241], 'euler43': [1, 0, -123670, 0, 6321363049], 'euler47': [1, 0, -142110, 0, 10779215329], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, -183510, 0, 22164361129], 'euler59': [1, -200, 420758, -41075800, 42180533641], 'euler61': [1, -1484, 1004526, -336839804, 51520374361], 'euler67': [1, 0, -594470, 0, 90458382169], 'euler7': [1, 0, -110, 0, 117649], 'euler71': [1, -656, 823406, -234789616, 128100283921], 'euler73': [1, 0, -776590, 0, 151334226289], 'euler79': [1, -480, 1043678, -236658720, 243087455521], 'euler83': [1, 0, 325370, 0, 326940373369], 'euler89': [1, -660, 1518838, -465279540, 496981290961], 'euler97': [1, 0, -1075390, 0, 832972004929], 'euler_factors': [[1, 0, -15, 0, 64], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, -110, 0, 117649], [1, 104, 5366, 138424, 1771561], [1, 0, -3910, 0, 4826809], [1, 0, -9630, 0, 24137569], [1, -40, 14118, -274360, 47045881], [1, 0, 3890, 0, 148035889], [1, -460, 101678, -11218940, 594823321], [1, 576, 142526, 17159616, 887503681], [1, 0, -100150, 0, 2565726409], [1, 244, 152726, 16816724, 4750104241], [1, 0, -123670, 0, 6321363049], [1, 0, -142110, 0, 10779215329], [1, 0, -183510, 0, 22164361129], [1, -200, 420758, -41075800, 42180533641], [1, -1484, 1004526, -336839804, 51520374361], [1, 0, -594470, 0, 90458382169], [1, -656, 823406, -234789616, 128100283921], [1, 0, -776590, 0, 151334226289], [1, -480, 1043678, -236658720, 243087455521], [1, 0, 325370, 0, 326940373369], [1, -660, 1518838, -465279540, 496981290961], [1, 0, -1075390, 0, 832972004929]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/4/b/e'], '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': '4-15e4-1.1-c3e2-0-2', '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': '4-15e4-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 2041590200024138205, 'z1': {'__RealLiteral__': 0, 'data': '0.68620481326327830775892603488', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '869867943412694818632822237243,2551707628207715927103078552094', 'Lhash_array': ['869867943412694818632822237243', '2551707628207715927103078552094'], 'label': '4-15e4-1.1-c3e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/4/b/e'}