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lfunc_lfunctions • Show schema
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{'Lhash': '1840030837443295318614571854716,2445587766404938103212319462280', 'a10': 0, 'a2': 0, 'a3': -4, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -4, 'a8': 0, 'a9': -18, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 556.9960614920828, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '400.1', 'coefficient_field': '1.1.1.1', 'conductor': 160000, 'conductor_radical': 10, 'degree': 4, 'euler_factors': [[1], [1, 4, 34, 108, 729], [1], [1, 4, 474, 1372, 117649], [1, 40, 1526, 53240, 1771561], [1, -104, 7002, -228488, 4826809], [1, -96, 5986, -471648, 24137569], [1, 40, 12582, 274360, 47045881], [1, 284, 40442, 3455428, 148035889], [1, 140, 47534, 3414460, 594823321], [1, 192, 13502, 5719872, 887503681], [1, -200, 83562, -10130600, 2565726409], [1, 524, 203030, 36114604, 4750104241], [1, 372, 183026, 29576604, 6321363049], [1, 84, 108010, 8721132, 10779215329], [1, 296, 29258, 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{'algebraic': True, 'analytic_conductor': 556.9960614920828, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 160000, 'conductor_radical': 10, 'degree': 4, 'dirichlet_coefficients': [1, 0, -4, 0, 0, 0, -4, 0, -18, 0, -40, 0, 104, 0, 0, 0, 96, 0, -40, 0, 16, 0, -284, 0, 0, 0, 100, 0, -140, 0, -192, 0, 160, 0, 0, 0, 200, 0, -416, 0, -524, 0, -372, 0, 0, 0, -84, 0, -458, 0, -384, 0, -296, 0, 0, 0, 160, 0, -696, 0, -692, 0, 72, 0, 0, 0, -316, 0, 1136, 0, -688, 0, -656, 0, 0, 0, 160, 0, 736, 0, -85, 0, 1628, 0, 0, 0, 560, 0, -660, 0, -416, 0, 768, 0, 0, 0, 896, 0, 720, 0], 'euler11': [1, 40, 1526, 53240, 1771561], 'euler13': [1, -104, 7002, -228488, 4826809], 'euler17': [1, -96, 5986, -471648, 24137569], 'euler19': [1, 40, 12582, 274360, 47045881], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 284, 40442, 3455428, 148035889], 'euler29': [1, 140, 47534, 3414460, 594823321], 'euler3': [1, 4, 34, 108, 729], 'euler31': [1, 192, 13502, 5719872, 887503681], 'euler37': [1, -200, 83562, -10130600, 2565726409], 'euler41': [1, 524, 203030, 36114604, 4750104241], 'euler43': [1, 372, 183026, 29576604, 6321363049], 'euler47': [1, 84, 108010, 8721132, 10779215329], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 296, 29258, 44067592, 22164361129], 'euler59': [1, 696, 346006, 142943784, 42180533641], 'euler61': [1, 692, 554862, 157070852, 51520374361], 'euler67': [1, 316, 625314, 95041108, 90458382169], 'euler7': [1, 4, 474, 1372, 117649], 'euler71': [1, 688, 809582, 246242768, 128100283921], 'euler73': [1, 656, 682482, 255195152, 151334226289], 'euler79': [1, -736, 1115358, -362876704, 243087455521], 'euler83': [1, -1628, 1748546, -930869236, 326940373369], 'euler89': [1, 660, 1463542, 465279540, 496981290961], 'euler97': [1, -896, 1987650, -817755008, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0], [1, 4, 34, 108, 729], [1, 0, 0, 0, 0], [1, 4, 474, 1372, 117649], [1, 40, 1526, 53240, 1771561], [1, -104, 7002, -228488, 4826809], [1, -96, 5986, -471648, 24137569], [1, 40, 12582, 274360, 47045881], [1, 284, 40442, 3455428, 148035889], [1, 140, 47534, 3414460, 594823321], [1, 192, 13502, 5719872, 887503681], [1, -200, 83562, -10130600, 2565726409], [1, 524, 203030, 36114604, 4750104241], [1, 372, 183026, 29576604, 6321363049], [1, 84, 108010, 8721132, 10779215329], [1, 296, 29258, 44067592, 22164361129], [1, 696, 346006, 142943784, 42180533641], [1, 692, 554862, 157070852, 51520374361], [1, 316, 625314, 95041108, 90458382169], [1, 688, 809582, 246242768, 128100283921], [1, 656, 682482, 255195152, 151334226289], [1, -736, 1115358, -362876704, 243087455521], [1, -1628, 1748546, -930869236, 326940373369], [1, 660, 1463542, 465279540, 496981290961], [1, -896, 1987650, -817755008, 832972004929]], 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/400/4/a/v'], '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': '4-20e4-1.1-c3e2-0-15', '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': 2, 'prelabel': '4-20e4-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.858061753651991, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 963979266983061368, 'z1': {'__RealLiteral__': 0, 'data': '1.45152839206009436862115203979', 'prec': 103}}
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{'Lhash': '1840030837443295318614571854716,2445587766404938103212319462280', 'Lhash_array': ['1840030837443295318614571854716', '2445587766404938103212319462280'], 'label': '4-20e4-1.1-c3e2-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/400/4/a/v'}