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lfunc_lfunctions • Show schema
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{'Lhash': '2153180467097959034346691519173,2213699306107880963313100672468', 'a10': 0, 'a2': 0, 'a3': 6, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 27, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2053.3102810844143, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -6, 9]]], 'bad_primes': [2, 3], 'central_character': '768.1', 'coefficient_field': '1.1.1.1', 'conductor': 589824, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1, -6, 9], [1, 0, 242, 0, 15625], [1, 0, 486, 0, 117649], [1, 40, 3062, 53240, 1771561], [1, 0, 2826, 0, 4826809], [1, 68, 10982, 334084, 24137569], [1, 104, 16422, 713336, 47045881], [1, 0, 20462, 0, 148035889], [1, 0, 8450, 0, 594823321], [1, 0, 47414, 0, 887503681], [1, 0, 27578, 0, 2565726409], [1, 52, 138518, 3583892, 4750104241], [1, 504, 222518, 40071528, 6321363049], [1, 0, 88574, 0, 10779215329], [1, 0, -166894, 0, 22164361129], [1, 728, 543254, 149515912, 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'8.628915338187413241312700958106212', '9.395679435126117750119942833625567', '9.589992128455905878883699195049754'], 'prelabel': '4-768e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.731527826905926, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3e2-0', 'trace_hash': 251370910912409683, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.69855989237909698989824609808', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.74630083850338868463303793054', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.70333168971052675208965721674', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2053.3102810844143, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 589824, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 6, 0, 0, 0, 0, 0, 27, 0, -40, 0, 0, 0, 0, 0, -68, 0, -104, 0, 0, 0, 0, 0, -242, 0, 108, 0, 0, 0, 0, 0, -240, 0, 0, 0, 0, 0, 0, 0, -52, 0, -504, 0, 0, 0, 0, 0, -486, 0, -408, 0, 0, 0, 0, 0, -624, 0, -728, 0, 0, 0, 0, 0, 0, 0, -1256, 0, 0, 0, 0, 0, 676, 0, -1452, 0, 0, 0, 0, 0, 405, 0, -2072, 0, 0, 0, 0, 0, 468, 0, 0, 0, 0, 0, 0, 0, -356, 0, -1080, 0], 'euler11': [1, 40, 3062, 53240, 1771561], 'euler13': [1, 0, 2826, 0, 4826809], 'euler17': [1, 68, 10982, 334084, 24137569], 'euler19': [1, 104, 16422, 713336, 47045881], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 20462, 0, 148035889], 'euler29': [1, 0, 8450, 0, 594823321], 'euler3': [1, -6, 9, 0, 0], 'euler31': [1, 0, 47414, 0, 887503681], 'euler37': [1, 0, 27578, 0, 2565726409], 'euler41': [1, 52, 138518, 3583892, 4750104241], 'euler43': [1, 504, 222518, 40071528, 6321363049], 'euler47': [1, 0, 88574, 0, 10779215329], 'euler5': [1, 0, 242, 0, 15625], 'euler53': [1, 0, -166894, 0, 22164361129], 'euler59': [1, 728, 543254, 149515912, 42180533641], 'euler61': [1, 0, -86838, 0, 51520374361], 'euler67': [1, 1256, 995910, 377758328, 90458382169], 'euler7': [1, 0, 486, 0, 117649], 'euler71': [1, 0, 604430, 0, 128100283921], 'euler73': [1, -676, 892278, -262975492, 151334226289], 'euler79': [1, 0, 363350, 0, 243087455521], 'euler83': [1, 2072, 2216870, 1184742664, 326940373369], 'euler89': [1, -468, 1464694, -329925492, 496981290961], 'euler97': [1, 356, 1857030, 324911588, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0], [1, -6, 9, 0, 0], [1, 0, 242, 0, 15625], [1, 0, 486, 0, 117649], [1, 40, 3062, 53240, 1771561], [1, 0, 2826, 0, 4826809], [1, 68, 10982, 334084, 24137569], [1, 104, 16422, 713336, 47045881], [1, 0, 20462, 0, 148035889], [1, 0, 8450, 0, 594823321], [1, 0, 47414, 0, 887503681], [1, 0, 27578, 0, 2565726409], [1, 52, 138518, 3583892, 4750104241], [1, 504, 222518, 40071528, 6321363049], [1, 0, 88574, 0, 10779215329], [1, 0, -166894, 0, 22164361129], [1, 728, 543254, 149515912, 42180533641], [1, 0, -86838, 0, 51520374361], [1, 1256, 995910, 377758328, 90458382169], [1, 0, 604430, 0, 128100283921], [1, -676, 892278, -262975492, 151334226289], [1, 0, 363350, 0, 243087455521], [1, 2072, 2216870, 1184742664, 326940373369], [1, -468, 1464694, -329925492, 496981290961], [1, 356, 1857030, 324911588, 832972004929]], 'index': 37, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/768/4/a/m'], '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': '4-768e2-1.1-c3e2-0-37', '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': '4-768e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.731527826905926, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 251370910912409683, 'z1': {'__RealLiteral__': 0, 'data': '1.69855989237909698989824609808', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2153180467097959034346691519173,2213699306107880963313100672468', 'Lhash_array': ['2153180467097959034346691519173', '2213699306107880963313100672468'], 'label': '4-768e2-1.1-c3e2-0-37', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/768/4/a/m'}