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lfunc_lfunctions • Show schema
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{'Lhash': '1596816693131454503578683760516,1984040850948167279819656163614', '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, 142, 0, 15625], [1, 0, 674, 0, 117649], [1, 0, 2662, 0, 1771561], [1, 0, 1322, 0, 4826809], [1, 180, 17926, 884340, 24137569], [1, -232, 27174, -1591288, 47045881], [1, 0, 13534, 0, 148035889], [1, 0, -18722, 0, 594823321], [1, 0, -31246, 0, 887503681], [1, 0, 100106, 0, 2565726409], [1, -108, 140758, -7443468, 4750104241], [1, -40, 159414, -3180280, 6321363049], [1, 0, 51694, 0, 10779215329], [1, 0, 59182, 0, 22164361129], [1, -648, 515734, -133085592, 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'8.972122515411266132223183645087345', '9.496020693762901509601645384803794', '9.608973637026612454610298084310892'], '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': 156803287420832205, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.25966626201570182391997511822', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.56513226167443779892859890300', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.60590554348838389545866181964', '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, 0, 0, 0, 0, 0, 0, -180, 0, 232, 0, 0, 0, 0, 0, -142, 0, -108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 108, 0, 40, 0, 0, 0, 0, 0, -674, 0, 1080, 0, 0, 0, 0, 0, -1392, 0, 648, 0, 0, 0, 0, 0, 0, 0, -232, 0, 0, 0, 0, 0, -2212, 0, 852, 0, 0, 0, 0, 0, 405, 0, -2304, 0, 0, 0, 0, 0, -1836, 0, 0, 0, 0, 0, 0, 0, 380, 0, 0, 0], 'euler11': [1, 0, 2662, 0, 1771561], 'euler13': [1, 0, 1322, 0, 4826809], 'euler17': [1, 180, 17926, 884340, 24137569], 'euler19': [1, -232, 27174, -1591288, 47045881], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 13534, 0, 148035889], 'euler29': [1, 0, -18722, 0, 594823321], 'euler3': [1, 6, 9, 0, 0], 'euler31': [1, 0, -31246, 0, 887503681], 'euler37': [1, 0, 100106, 0, 2565726409], 'euler41': [1, -108, 140758, -7443468, 4750104241], 'euler43': [1, -40, 159414, -3180280, 6321363049], 'euler47': [1, 0, 51694, 0, 10779215329], 'euler5': [1, 0, 142, 0, 15625], 'euler53': [1, 0, 59182, 0, 22164361129], 'euler59': [1, -648, 515734, -133085592, 42180533641], 'euler61': [1, 0, 123290, 0, 51520374361], 'euler67': [1, 232, 614982, 69777016, 90458382169], 'euler7': [1, 0, 674, 0, 117649], 'euler71': [1, 0, -497666, 0, 128100283921], 'euler73': [1, 2212, 2001270, 860505604, 151334226289], 'euler79': [1, 0, 963890, 0, 243087455521], 'euler83': [1, 2304, 2470678, 1317397248, 326940373369], 'euler89': [1, 1836, 2252662, 1294323084, 496981290961], 'euler97': [1, -380, 1861446, -346815740, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0], [1, 6, 9, 0, 0], [1, 0, 142, 0, 15625], [1, 0, 674, 0, 117649], [1, 0, 2662, 0, 1771561], [1, 0, 1322, 0, 4826809], [1, 180, 17926, 884340, 24137569], [1, -232, 27174, -1591288, 47045881], [1, 0, 13534, 0, 148035889], [1, 0, -18722, 0, 594823321], [1, 0, -31246, 0, 887503681], [1, 0, 100106, 0, 2565726409], [1, -108, 140758, -7443468, 4750104241], [1, -40, 159414, -3180280, 6321363049], [1, 0, 51694, 0, 10779215329], [1, 0, 59182, 0, 22164361129], [1, -648, 515734, -133085592, 42180533641], [1, 0, 123290, 0, 51520374361], [1, 232, 614982, 69777016, 90458382169], [1, 0, -497666, 0, 128100283921], [1, 2212, 2001270, 860505604, 151334226289], [1, 0, 963890, 0, 243087455521], [1, 2304, 2470678, 1317397248, 326940373369], [1, 1836, 2252662, 1294323084, 496981290961], [1, -380, 1861446, -346815740, 832972004929]], 'index': 32, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/768/4/a/g'], '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-c3e2-0-32', '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': 156803287420832205, 'z1': {'__RealLiteral__': 0, 'data': '1.25966626201570182391997511822', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1596816693131454503578683760516,1984040850948167279819656163614', 'Lhash_array': ['1596816693131454503578683760516', '1984040850948167279819656163614'], 'label': '4-768e2-1.1-c3e2-0-32', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/768/4/a/g'}