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lfunc_lfunctions • Show schema
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{'Lhash': '1097489635908927374099103362452', 'a10': 0, 'a2': 0, 'a3': -3, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': -5, 'a8': 0, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.035981290937706, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [17, [1, -1]], [59, [1, 1]]], 'bad_primes': [2, 17, 59], 'central_character': '4012.1', 'coefficient_field': '1.1.1.1', 'conductor': 4012, 'conductor_radical': 2006, 'degree': 2, 'euler_factors': [[1], [1, 3, 3], [1, 1, 5], [1, 5, 7], [1, 2, 11], [1, -4, 13], [1, -1], [1, 3, 19], [1, 4, 23], [1, 3, 29], [1, -8, 31], [1, 0, 37], [1, -3, 41], [1, -4, 43], [1, -8, 47], [1, -7, 53], [1, 1], [1, -10, 61], [1, -10, 67], [1, 8, 71], [1, 10, 73], [1, -13, 79], [1, 4, 83], [1, -14, 89], [1, -2, 97], [1, -2, 101], [1, 16, 103], [1, 3, 107], [1, -2, 109], [1, 12, 113]], 'euler_factors_factorization': [[1], [[[1, 3, 3], 1]], [[[1, 1, 5], 1]], [[[1, 5, 7], 1]], [[[1, 2, 11], 1]], [[[1, -4, 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0.4357079939672152, 0.6414236993704322, 0.7918467477831795, 0.8804309837225627, 0.9041549541573103, 0.863702115593338, 0.7634355025330267, 0.6111655756286938], 'positive_zeros': ['0.865766667653795111763984925961491', '2.49870997660020956877328607924225', '3.75458992923721340994900991768284', '4.14700144449420769146954143752872', '5.36925875781838972355737971398616', '6.03188896603336529912461647418279', '6.32903379197905050458300817697657', '7.08614803891019696892062331006484', '7.903300837174390911035528850887755'], 'prelabel': '2-4012-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.660033682844803, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 222756878670368151, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.865766667653795111763984925961', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.49870997660020956877328607924', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.75458992923721340994900991768', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.035981290937706, 'bad_primes': [2, 17, 59], 'central_character': '1.1', 'conductor': 4012, 'conductor_radical': 2006, 'degree': 2, 'dirichlet_coefficients': [1, 0, -3, 0, -1, 0, -5, 0, 6, 0, -2, 0, 4, 0, 3, 0, 1, 0, -3, 0, 15, 0, -4, 0, -4, 0, -9, 0, -3, 0, 8, 0, 6, 0, 5, 0, 0, 0, -12, 0, 3, 0, 4, 0, -6, 0, 8, 0, 18, 0, -3, 0, 7, 0, 2, 0, 9, 0, -1, 0, 10, 0, -30, 0, -4, 0, 10, 0, 12, 0, -8, 0, -10, 0, 12, 0, 10, 0, 13, 0, 9, 0, -4, 0, -1, 0, 9, 0, 14, 0, -20, 0, -24, 0, 3, 0, 2, 0, -12, 0], 'euler11': [1, 2, 11], 'euler13': [1, -4, 13], 'euler17': [1, -1, 0], 'euler19': [1, 3, 19], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, 3, 29], 'euler3': [1, 3, 3], 'euler31': [1, -8, 31], 'euler37': [1, 0, 37], 'euler41': [1, -3, 41], 'euler43': [1, -4, 43], 'euler47': [1, -8, 47], 'euler5': [1, 1, 5], 'euler53': [1, -7, 53], 'euler59': [1, 1, 0], 'euler61': [1, -10, 61], 'euler67': [1, -10, 67], 'euler7': [1, 5, 7], 'euler71': [1, 8, 71], 'euler73': [1, 10, 73], 'euler79': [1, -13, 79], 'euler83': [1, 4, 83], 'euler89': [1, -14, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 3, 3], [1, 1, 5], [1, 5, 7], [1, 2, 11], [1, -4, 13], [1, -1, 0], [1, 3, 19], [1, 4, 23], [1, 3, 29], [1, -8, 31], [1, 0, 37], [1, -3, 41], [1, -4, 43], [1, -8, 47], [1, -7, 53], [1, 1, 0], [1, -10, 61], [1, -10, 67], [1, 8, 71], [1, 10, 73], [1, -13, 79], [1, 4, 83], [1, -14, 89], [1, -2, 97]], 'index': 22, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/4012/b', 'ModularForm/GL2/Q/holomorphic/4012/2/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/4012/2/a/b'], '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': '2-4012-1.1-c1-0-22', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-4012-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.660033682844803, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 222756878670368151, 'z1': {'__RealLiteral__': 0, 'data': '0.865766667653795111763984925961', 'prec': 107}}
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lfunc_instances • Show schema
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id: 20260961
{'Lhash': '1097489635908927374099103362452', 'Lhash_array': ['1097489635908927374099103362452'], 'label': '2-4012-1.1-c1-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4012/2/a/b'}
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id: 24564063
{'Lhash': '1097489635908927374099103362452', 'Lhash_array': ['1097489635908927374099103362452'], 'label': '2-4012-1.1-c1-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4012/2/a/b/1/1'}
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id: 91219
{'Lhash': '222756878670368151', 'Lhash_array': ['222756878670368151'], 'label': '2-4012-1.1-c1-0-22', 'type': 'ECQ', 'url': 'EllipticCurve/Q/4012/b'}