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lfunc_lfunctions • Show schema
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{'Lhash': '816482757193698276513278505527,1284762407349882927943190395292', 'a10': 0, 'a2': -2, 'a3': 0, 'a4': -13, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 44, 'a9': -10, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 628.7963350437966, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[5, [1]], [17, [1, -34, 4913]]], 'bad_primes': [5, 17], 'central_character': '425.1', 'coefficient_field': '1.1.1.1', 'conductor': 180625, 'conductor_radical': 85, 'degree': 4, 'euler_factors': [[1, 2, 17, 16, 64], [1, 0, 10, 0, 729], [1], [1, 0, -490, 0, 117649], [1, 0, -2262, 0, 1771561], [1, -116, 7758, -254852, 4826809], [1, -34, 4913], [1, -160, 20118, -1097440, 47045881], [1, 0, -10410, 0, 148035889], [1, 0, -32902, 0, 594823321], [1, 0, -54682, 0, 887503681], [1, 0, -83350, 0, 2565726409], [1, 0, -127842, 0, 4750104241], [1, 544, 232998, 43251808, 6321363049], [1, -928, 422942, -96347744, 10779215329], [1, 1284, 709918, 191158068, 22164361129], [1, 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{'algebraic': True, 'analytic_conductor': 628.7963350437966, 'bad_primes': [5, 17], 'central_character': '1.1', 'conductor': 180625, 'conductor_radical': 85, 'degree': 4, 'dirichlet_coefficients': [1, -2, 0, -13, 0, 0, 0, 44, -10, 0, 0, 0, 116, 0, 0, 101, 34, 20, 160, 0, 0, 0, 0, 0, 0, -232, 0, 0, 0, 0, 0, -614, 0, -68, 0, 130, 0, -320, 0, 0, 0, 0, -544, 0, 0, 0, 928, 0, 490, 0, 0, -1508, -1284, 0, 0, 0, 0, 0, -360, 0, 0, 0, 0, -361, 0, 0, 1848, -442, 0, 0, 0, -440, 0, 0, 0, -2080, 0, 0, 0, 0, -629, 0, -1104, 0, 0, 1088, 0, 0, 2980, 0, 0, 0, 0, -1856, 0, 0, 0, -980, 0, 0], 'euler11': [1, 0, -2262, 0, 1771561], 'euler13': [1, -116, 7758, -254852, 4826809], 'euler17': [1, -34, 4913, 0, 0], 'euler19': [1, -160, 20118, -1097440, 47045881], 'euler2': [1, 2, 17, 16, 64], 'euler23': [1, 0, -10410, 0, 148035889], 'euler29': [1, 0, -32902, 0, 594823321], 'euler3': [1, 0, 10, 0, 729], 'euler31': [1, 0, -54682, 0, 887503681], 'euler37': [1, 0, -83350, 0, 2565726409], 'euler41': [1, 0, -127842, 0, 4750104241], 'euler43': [1, 544, 232998, 43251808, 6321363049], 'euler47': [1, -928, 422942, -96347744, 10779215329], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 1284, 709918, 191158068, 22164361129], 'euler59': [1, 360, 443158, 73936440, 42180533641], 'euler61': [1, 0, -441862, 0, 51520374361], 'euler67': [1, -1848, 1455302, -555810024, 90458382169], 'euler7': [1, 0, -490, 0, 117649], 'euler71': [1, 0, -707722, 0, 128100283921], 'euler73': [1, 0, -92450, 0, 151334226289], 'euler79': [1, 0, 793478, 0, 243087455521], 'euler83': [1, 1104, 1448278, 631252848, 326940373369], 'euler89': [1, -2980, 3630038, -2100807620, 496981290961], 'euler97': [1, 0, 68030, 0, 832972004929], 'euler_factors': [[1, 2, 17, 16, 64], [1, 0, 10, 0, 729], [1, 0, 0, 0, 0], [1, 0, -490, 0, 117649], [1, 0, -2262, 0, 1771561], [1, -116, 7758, -254852, 4826809], [1, -34, 4913, 0, 0], [1, -160, 20118, -1097440, 47045881], [1, 0, -10410, 0, 148035889], [1, 0, -32902, 0, 594823321], [1, 0, -54682, 0, 887503681], [1, 0, -83350, 0, 2565726409], [1, 0, -127842, 0, 4750104241], [1, 544, 232998, 43251808, 6321363049], [1, -928, 422942, -96347744, 10779215329], [1, 1284, 709918, 191158068, 22164361129], [1, 360, 443158, 73936440, 42180533641], [1, 0, -441862, 0, 51520374361], [1, -1848, 1455302, -555810024, 90458382169], [1, 0, -707722, 0, 128100283921], [1, 0, -92450, 0, 151334226289], [1, 0, 793478, 0, 243087455521], [1, 1104, 1448278, 631252848, 326940373369], [1, -2980, 3630038, -2100807620, 496981290961], [1, 0, 68030, 0, 832972004929]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/425/4/d/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': '4-425e2-1.1-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': '4-425e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.00757543652013, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 838164653535209648, 'z1': {'__RealLiteral__': 0, 'data': '0.64409132693716841096213039130', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '816482757193698276513278505527,1284762407349882927943190395292', 'Lhash_array': ['816482757193698276513278505527', '1284762407349882927943190395292'], 'factors': ['2-425-17.16-c3-0-24', '2-425-17.16-c3-0-44'], 'label': '4-425e2-1.1-c3e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/425/4/d/a'}