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lfunc_lfunctions • Show schema
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{'Lhash': '2589292854956864502558643150331', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': -3, 'a6': 0, 'a7': -1, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.7098088857877, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [19, [1, 1]]], 'bad_primes': [2, 19], 'central_character': '1216.1', 'coefficient_field': '1.1.1.1', 'conductor': 1216, 'conductor_radical': 38, 'degree': 2, 'euler_factors': [[1], [1, -2, 3], [1, 3, 5], [1, 1, 7], [1, 3, 11], [1, -4, 13], [1, 3, 17], [1, 1], [1, 0, 23], [1, 6, 29], [1, 4, 31], [1, 2, 37], [1, 6, 41], [1, -1, 43], [1, 3, 47], [1, 12, 53], [1, -6, 59], [1, -1, 61], [1, -4, 67], [1, -6, 71], [1, 7, 73], [1, -8, 79], [1, 12, 83], [1, -12, 89], [1, -8, 97], [1, 6, 101], [1, -14, 103], [1, -18, 107], [1, -16, 109], [1, -6, 113]], 'euler_factors_factorization': [[1], [[[1, -2, 3], 1]], [[[1, 3, 5], 1]], [[[1, 1, 7], 1]], [[[1, 3, 11], 1]], [[[1, -4, 13], 1]], [[[1, 3, 17], 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-1.303170650709808, -0.884131158698986, -0.4518606818012525, -0.03422639227359992, 0.34265569198689166, 0.6562312473511572, 0.8890638299923058, 1.0300248768370373, 1.0750301101480588], 'positive_zeros': ['2.04259190544357015606449170426144', '3.31935920587958999413340629738558', '3.67310116806022314895429635564089', '4.80419327140120764096716079767299', '6.05813289271022268292942638230791', '7.15811652768508964807251071197379', '7.86885586734404145925295723068407', '8.457332600420497477897703269253053', '9.035139763634884351001508227660721'], 'prelabel': '2-1216-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.11605662429098, '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': 2107969557023941800, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.04259190544357015606449170426', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.31935920587958999413340629739', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.67310116806022314895429635564', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.7098088857877, 'bad_primes': [2, 19], 'central_character': '1.1', 'conductor': 1216, 'conductor_radical': 38, 'degree': 2, 'dirichlet_coefficients': [1, 0, 2, 0, -3, 0, -1, 0, 1, 0, -3, 0, 4, 0, -6, 0, -3, 0, -1, 0, -2, 0, 0, 0, 4, 0, -4, 0, -6, 0, -4, 0, -6, 0, 3, 0, -2, 0, 8, 0, -6, 0, 1, 0, -3, 0, -3, 0, -6, 0, -6, 0, -12, 0, 9, 0, -2, 0, 6, 0, 1, 0, -1, 0, -12, 0, 4, 0, 0, 0, 6, 0, -7, 0, 8, 0, 3, 0, 8, 0, -11, 0, -12, 0, 9, 0, -12, 0, 12, 0, -4, 0, -8, 0, 3, 0, 8, 0, -3, 0], 'euler11': [1, 3, 11], 'euler13': [1, -4, 13], 'euler17': [1, 3, 17], 'euler19': [1, 1, 0], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, 6, 29], 'euler3': [1, -2, 3], 'euler31': [1, 4, 31], 'euler37': [1, 2, 37], 'euler41': [1, 6, 41], 'euler43': [1, -1, 43], 'euler47': [1, 3, 47], 'euler5': [1, 3, 5], 'euler53': [1, 12, 53], 'euler59': [1, -6, 59], 'euler61': [1, -1, 61], 'euler67': [1, -4, 67], 'euler7': [1, 1, 7], 'euler71': [1, -6, 71], 'euler73': [1, 7, 73], 'euler79': [1, -8, 79], 'euler83': [1, 12, 83], 'euler89': [1, -12, 89], 'euler97': [1, -8, 97], 'euler_factors': [[1, 0, 0], [1, -2, 3], [1, 3, 5], [1, 1, 7], [1, 3, 11], [1, -4, 13], [1, 3, 17], [1, 1, 0], [1, 0, 23], [1, 6, 29], [1, 4, 31], [1, 2, 37], [1, 6, 41], [1, -1, 43], [1, 3, 47], [1, 12, 53], [1, -6, 59], [1, -1, 61], [1, -4, 67], [1, -6, 71], [1, 7, 73], [1, -8, 79], [1, 12, 83], [1, -12, 89], [1, -8, 97]], 'index': 32, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1216/o', 'ModularForm/GL2/Q/holomorphic/1216/2/a/o/1/1', 'ModularForm/GL2/Q/holomorphic/1216/2/a/o'], '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': '2-1216-1.1-c1-0-32', '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': '2-1216-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.11605662429098, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2107969557023941800, 'z1': {'__RealLiteral__': 0, 'data': '2.04259190544357015606449170426', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20709631
{'Lhash': '2589292854956864502558643150331', 'Lhash_array': ['2589292854956864502558643150331'], 'label': '2-1216-1.1-c1-0-32', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1216/2/a/o'}
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id: 24552236
{'Lhash': '2589292854956864502558643150331', 'Lhash_array': ['2589292854956864502558643150331'], 'label': '2-1216-1.1-c1-0-32', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1216/2/a/o/1/1'}
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id: 38338
{'Lhash': '2107969557023941800', 'Lhash_array': ['2107969557023941800'], 'label': '2-1216-1.1-c1-0-32', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1216/o'}