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lfunc_lfunctions • Show schema
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{'Lhash': '550406033640688074679757721538,989988457604225829432687902865', 'a10': 10, 'a2': -2, 'a3': 0, 'a4': 0, 'a5': -5, 'a6': 0, 'a7': -14, 'a8': 8, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2284.031974655972, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2, 4]], [3, [1]], [5, [1, 5, 25]]], 'bad_primes': [2, 3, 5], 'central_character': '810.1', 'coefficient_field': '1.1.1.1', 'conductor': 656100, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1, 2, 4], [1], [1, 5, 25], [1, 14, -147, 4802, 117649], [1, -6, -1295, -7986, 1771561], [1, 68, 2427, 149396, 4826809], [1, 156, 15910, 766428, 24137569], [1, -88, 15654, -603592, 47045881], [1, -120, 2233, -1460040, 148035889], [1, -126, -8513, -3073014, 594823321], [1, -244, 29745, -7269004, 887503681], [1, 608, 193722, 30797024, 2565726409], [1, 480, 161479, 33082080, 4750104241], [1, 104, -68691, 8268728, 6321363049], [1, -600, 256177, -62293800, 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'positive_zeros': ['0.43419380193689987061901834077402', '0.78096319082402285598252826912308', '1.93059209658484318798592657299478', '2.40494693836797730481215758587939', '2.99504874152822162071524140062687', '3.64036039217303153172313992456954', '4.12057393426852355791066510728957', '4.84456105884457559984360976996866', '5.06998141274431255076505812897439', '5.52153334075868838309731534712305', '6.60112852050669371496419690327733', '6.72567292619690724621766534315102', '6.96378722362183589642910148184073', '7.44341749514887886407294045500221', '8.048376392844444442410170537611534', '8.515850179315590759417505213659166', '8.934941243252355244726807936089112', '9.035196337251817847602833911428767', '9.723226220786859470012486102079760', '9.953484201120309725964394893902026'], 'prelabel': '4-810e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.91314306988145, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e2-0', 'trace_hash': 1985478923386419068, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.43419380193689987061901834077', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.78096319082402285598252826912', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.93059209658484318798592657299', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 2284.031974655972, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 656100, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, -2, 0, 0, -5, 0, -14, 8, 0, 10, 6, 0, -68, 28, 0, -16, -156, 0, 88, 0, 0, -12, 120, 0, 0, 136, 0, 0, 126, 0, 244, 0, 0, 312, 70, 0, -608, -176, 0, -40, -480, 0, -104, 0, 0, -240, 600, 0, 343, 0, 0, 0, 516, 0, -30, -112, 0, -252, 534, 0, -362, -488, 0, 64, 340, 0, 268, 0, 0, -140, 1944, 0, 940, 1216, 0, 0, -84, 0, -1244, 80, 0, 960, 396, 0, 780, 208, 0, 48, 1944, 0, 952, 0, 0, -1200, -440, 0, 46, -686, 0, 0], 'euler11': [1, -6, -1295, -7986, 1771561], 'euler13': [1, 68, 2427, 149396, 4826809], 'euler17': [1, 156, 15910, 766428, 24137569], 'euler19': [1, -88, 15654, -603592, 47045881], 'euler2': [1, 2, 4, 0, 0], 'euler23': [1, -120, 2233, -1460040, 148035889], 'euler29': [1, -126, -8513, -3073014, 594823321], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -244, 29745, -7269004, 887503681], 'euler37': [1, 608, 193722, 30797024, 2565726409], 'euler41': [1, 480, 161479, 33082080, 4750104241], 'euler43': [1, 104, -68691, 8268728, 6321363049], 'euler47': [1, -600, 256177, -62293800, 10779215329], 'euler5': [1, 5, 25, 0, 0], 'euler53': [1, -516, 364318, -76820532, 22164361129], 'euler59': [1, -534, 79777, -109672386, 42180533641], 'euler61': [1, 362, -95937, 82167122, 51520374361], 'euler67': [1, -268, -228939, -80604484, 90458382169], 'euler7': [1, 14, -147, 4802, 117649], 'euler71': [1, -1944, 1660606, -695778984, 128100283921], 'euler73': [1, -940, 998934, -365675980, 151334226289], 'euler79': [1, 1244, 1054497, 613340516, 243087455521], 'euler83': [1, -396, -414971, -226427652, 326940373369], 'euler89': [1, -1944, 2354722, -1370459736, 496981290961], 'euler97': [1, -46, -910557, -41982958, 832972004929], 'euler_factors': [[1, 2, 4, 0, 0], [1, 0, 0, 0, 0], [1, 5, 25, 0, 0], [1, 14, -147, 4802, 117649], [1, -6, -1295, -7986, 1771561], [1, 68, 2427, 149396, 4826809], [1, 156, 15910, 766428, 24137569], [1, -88, 15654, -603592, 47045881], [1, -120, 2233, -1460040, 148035889], [1, -126, -8513, -3073014, 594823321], [1, -244, 29745, -7269004, 887503681], [1, 608, 193722, 30797024, 2565726409], [1, 480, 161479, 33082080, 4750104241], [1, 104, -68691, 8268728, 6321363049], [1, -600, 256177, -62293800, 10779215329], [1, -516, 364318, -76820532, 22164361129], [1, -534, 79777, -109672386, 42180533641], [1, 362, -95937, 82167122, 51520374361], [1, -268, -228939, -80604484, 90458382169], [1, -1944, 1660606, -695778984, 128100283921], [1, -940, 998934, -365675980, 151334226289], [1, 1244, 1054497, 613340516, 243087455521], [1, -396, -414971, -226427652, 326940373369], [1, -1944, 2354722, -1370459736, 496981290961], [1, -46, -910557, -41982958, 832972004929]], 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/810/4/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': '4-810e2-1.1-c3e2-0-13', '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': '4-810e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.91314306988145, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1985478923386419068, 'z1': {'__RealLiteral__': 0, 'data': '0.43419380193689987061901834077', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '550406033640688074679757721538,989988457604225829432687902865', 'Lhash_array': ['550406033640688074679757721538', '989988457604225829432687902865'], 'label': '4-810e2-1.1-c3e2-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/810/4/e/a'}