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lfunc_lfunctions • Show schema
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{'Lhash': '3093460584982003437685541537447', 'a10': -2, 'a2': 2, 'a3': 0, 'a4': 2, 'a5': -1, 'a6': 0, 'a7': 3, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [19, [1, 1]]], 'bad_primes': [3, 19], 'central_character': '171.1', 'coefficient_field': '1.1.1.1', 'conductor': 171, 'conductor_radical': 57, 'degree': 2, 'euler_factors': [[1, -2, 2], [1], [1, 1, 5], [1, -3, 7], [1, -3, 11], [1, 6, 13], [1, 3, 17], [1, 1], [1, 4, 23], [1, -10, 29], [1, -2, 31], [1, -8, 37], [1, -8, 41], [1, 1, 43], [1, 3, 47], [1, -6, 53], [1, 0, 59], [1, -7, 61], [1, -8, 67], [1, 12, 71], [1, 11, 73], [1, 0, 79], [1, 4, 83], [1, 10, 89], [1, 2, 97], [1, 2, 101], [1, -14, 103], [1, -2, 107], [1, -20, 109], [1, -6, 113]], 'euler_factors_factorization': [[[[1, -2, 2], 1]], [1], [[[1, 1, 5], 1]], [[[1, -3, 7], 1]], [[[1, -3, 11], 1]], [[[1, 6, 13], 1]], [[[1, 3, 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0.49020556403021226, 0.7846170870365697, 0.881256826585243, 0.7273724799070954, 0.3542024578747083, -0.13168926114020932, -0.5809934202759588, -0.848479237185462], 'positive_zeros': ['2.44031011733442394942262196333811', '4.20883425493377341015603476650541', '4.75227634922127063518685270995151', '6.12831923497636436478284774657284', '7.33179869161333338136909211766785', '8.513296718878561122779255009177796', '9.886397115513209246726221997817507', '11.42285722847365155593370717983036', '11.84438281704762988883998671737258', '12.70402288938109990188600775185270'], 'prelabel': '2-171-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1428964173338174884, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.44031011733442394942262196334', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.20883425493377341015603476651', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.75227634922127063518685270995', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'bad_primes': [3, 19], 'central_character': '1.1', 'conductor': 171, 'conductor_radical': 57, 'degree': 2, 'dirichlet_coefficients': [1, 2, 0, 2, -1, 0, 3, 0, 0, -2, 3, 0, -6, 6, 0, -4, -3, 0, -1, -2, 0, 6, -4, 0, -4, -12, 0, 6, 10, 0, 2, -8, 0, -6, -3, 0, 8, -2, 0, 0, 8, 0, -1, 6, 0, -8, -3, 0, 2, -8, 0, -12, 6, 0, -3, 0, 0, 20, 0, 0, 7, 4, 0, -8, 6, 0, 8, -6, 0, -6, -12, 0, -11, 16, 0, -2, 9, 0, 0, 4, 0, 16, -4, 0, 3, -2, 0, 0, -10, 0, -18, -8, 0, -6, 1, 0, -2, 4, 0, -8], 'euler11': [1, -3, 11], 'euler13': [1, 6, 13], 'euler17': [1, 3, 17], 'euler19': [1, 1, 0], 'euler2': [1, -2, 2], 'euler23': [1, 4, 23], 'euler29': [1, -10, 29], 'euler3': [1, 0, 0], 'euler31': [1, -2, 31], 'euler37': [1, -8, 37], 'euler41': [1, -8, 41], 'euler43': [1, 1, 43], 'euler47': [1, 3, 47], 'euler5': [1, 1, 5], 'euler53': [1, -6, 53], 'euler59': [1, 0, 59], 'euler61': [1, -7, 61], 'euler67': [1, -8, 67], 'euler7': [1, -3, 7], 'euler71': [1, 12, 71], 'euler73': [1, 11, 73], 'euler79': [1, 0, 79], 'euler83': [1, 4, 83], 'euler89': [1, 10, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, -2, 2], [1, 0, 0], [1, 1, 5], [1, -3, 7], [1, -3, 11], [1, 6, 13], [1, 3, 17], [1, 1, 0], [1, 4, 23], [1, -10, 29], [1, -2, 31], [1, -8, 37], [1, -8, 41], [1, 1, 43], [1, 3, 47], [1, -6, 53], [1, 0, 59], [1, -7, 61], [1, -8, 67], [1, 12, 71], [1, 11, 73], [1, 0, 79], [1, 4, 83], [1, 10, 89], [1, 2, 97]], 'index': 4, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/171/c', 'ModularForm/GL2/Q/holomorphic/171/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/171/2/a/c'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-171-1.1-c1-0-4', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-171-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1428964173338174884, 'z1': {'__RealLiteral__': 0, 'data': '2.44031011733442394942262196334', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10002594
{'Lhash': '3093460584982003437685541537447', 'Lhash_array': ['3093460584982003437685541537447'], 'label': '2-171-1.1-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/2/a/c'}
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id: 24547630
{'Lhash': '3093460584982003437685541537447', 'Lhash_array': ['3093460584982003437685541537447'], 'label': '2-171-1.1-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/2/a/c/1/1'}
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id: 21837
{'Lhash': '1428964173338174884', 'Lhash_array': ['1428964173338174884'], 'label': '2-171-1.1-c1-0-4', 'type': 'ECQ', 'url': 'EllipticCurve/Q/171/c'}