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lfunc_lfunctions • Show schema
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{'Lhash': '838850414989562270705955811701,4938547880503047761167019148596', 'a10': 54, 'a2': -3, 'a3': -3, 'a4': 8, 'a5': -18, 'a6': 9, 'a7': -2, 'a8': -45, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.294943809559112, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 3, 9]], [13, [1, -65, 2197]]], 'bad_primes': [3, 13], 'central_character': '39.1', 'coefficient_field': '1.1.1.1', 'conductor': 1521, 'conductor_radical': 39, 'degree': 4, 'euler_factors': [[1, 3, 1, 24, 64], [1, 3, 9], [1, 18, 331, 2250, 15625], [1, 2, -339, 686, 117649], [1, 30, -431, 39930, 1771561], [1, -65, 2197], [1, -111, 7408, -545343, 24137569], [1, -46, -4743, -315514, 47045881], [1, -6, -12131, -73002, 148035889], [1, -105, -13364, -2560845, 594823321], [1, 200, 69582, 5958200, 887503681], [1, 17, -50364, 861101, 2565726409], [1, -231, -15560, -15920751, 4750104241], [1, -514, 184689, -40866598, 6321363049], [1, 324, 233890, 33638652, 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'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3e2-0', 'trace_hash': 1891022624787187164, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.66173629771368750311017618197', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.07740421174496972295053312568', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.89582735149094349531468270883', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 5.294943809559112, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 1521, 'conductor_radical': 39, 'degree': 4, 'dirichlet_coefficients': [1, -3, -3, 8, -18, 9, -2, -45, 0, 54, -30, -24, 65, 6, 54, 135, 111, 0, 46, -144, 6, 90, 6, 135, -7, -195, 27, -16, 105, -162, -200, -360, 90, -333, 36, 0, -17, -138, -195, 810, 231, -18, 514, -240, 0, -18, -324, -405, 343, 21, -333, 520, 1278, -81, 540, 90, -138, -315, -600, 432, -233, 600, 0, 1513, -1170, -270, -926, 888, -18, -108, 930, 0, -506, 51, 21, 368, 60, 585, -2648, -2430, -81, -693, 1620, 48, -1998, -1542, -315, 1350, -498, 0, -130, 48, 600, 972, -828, 1080, -1358, -1029, 0, -56], 'euler11': [1, 30, -431, 39930, 1771561], 'euler13': [1, -65, 2197, 0, 0], 'euler17': [1, -111, 7408, -545343, 24137569], 'euler19': [1, -46, -4743, -315514, 47045881], 'euler2': [1, 3, 1, 24, 64], 'euler23': [1, -6, -12131, -73002, 148035889], 'euler29': [1, -105, -13364, -2560845, 594823321], 'euler3': [1, 3, 9, 0, 0], 'euler31': [1, 200, 69582, 5958200, 887503681], 'euler37': [1, 17, -50364, 861101, 2565726409], 'euler41': [1, -231, -15560, -15920751, 4750104241], 'euler43': [1, -514, 184689, -40866598, 6321363049], 'euler47': [1, 324, 233890, 33638652, 10779215329], 'euler5': [1, 18, 331, 2250, 15625], 'euler53': [1, -1278, 706075, -190264806, 22164361129], 'euler59': [1, 600, 154621, 123227400, 42180533641], 'euler61': [1, 233, -172692, 52886573, 51520374361], 'euler67': [1, 926, 556713, 278506538, 90458382169], 'euler7': [1, 2, -339, 686, 117649], 'euler71': [1, -930, 506989, -332857230, 128100283921], 'euler73': [1, 506, 842043, 196842602, 151334226289], 'euler79': [1, 2648, 2739054, 1305567272, 243087455521], 'euler83': [1, -1620, 1799674, -926294940, 326940373369], 'euler89': [1, 498, -456965, 351074562, 496981290961], 'euler97': [1, 1358, 931491, 1239409934, 832972004929], 'euler_factors': [[1, 3, 1, 24, 64], [1, 3, 9, 0, 0], [1, 18, 331, 2250, 15625], [1, 2, -339, 686, 117649], [1, 30, -431, 39930, 1771561], [1, -65, 2197, 0, 0], [1, -111, 7408, -545343, 24137569], [1, -46, -4743, -315514, 47045881], [1, -6, -12131, -73002, 148035889], [1, -105, -13364, -2560845, 594823321], [1, 200, 69582, 5958200, 887503681], [1, 17, -50364, 861101, 2565726409], [1, -231, -15560, -15920751, 4750104241], [1, -514, 184689, -40866598, 6321363049], [1, 324, 233890, 33638652, 10779215329], [1, -1278, 706075, -190264806, 22164361129], [1, 600, 154621, 123227400, 42180533641], [1, 233, -172692, 52886573, 51520374361], [1, 926, 556713, 278506538, 90458382169], [1, -930, 506989, -332857230, 128100283921], [1, 506, 842043, 196842602, 151334226289], [1, 2648, 2739054, 1305567272, 243087455521], [1, -1620, 1799674, -926294940, 326940373369], [1, 498, -456965, 351074562, 496981290961], [1, 1358, 931491, 1239409934, 832972004929]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/39/4/e/a'], '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': '4-39e2-1.1-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': '4-39e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.5169292963826246, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1891022624787187164, 'z1': {'__RealLiteral__': 0, 'data': '0.66173629771368750311017618197', 'prec': 103}}
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{'Lhash': '838850414989562270705955811701,4938547880503047761167019148596', 'Lhash_array': ['838850414989562270705955811701', '4938547880503047761167019148596'], 'label': '4-39e2-1.1-c3e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/39/4/e/a'}