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lfunc_lfunctions • Show schema
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{'Lhash': '3212351063431410795933612714663', 'a10': 1, 'a2': 1, 'a3': 0, 'a4': -1, 'a5': 1, 'a6': 0, 'a7': -4, 'a8': -3, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, -1]], [13, [1, 1]]], 'bad_primes': [3, 5, 13], 'central_character': '585.1', 'coefficient_field': '1.1.1.1', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'euler_factors': [[1, -1, 2], [1], [1, -1], [1, 4, 7], [1, 2, 11], [1, 1], [1, 2, 17], [1, 6, 19], [1, -6, 23], [1, 2, 29], [1, 10, 31], [1, 2, 37], [1, -6, 41], [1, -10, 43], [1, 4, 47], [1, 2, 53], [1, 6, 59], [1, -2, 61], [1, 4, 67], [1, 6, 71], [1, 6, 73], [1, 12, 79], [1, -16, 83], [1, 2, 89], [1, 2, 97], [1, -18, 101], [1, -2, 103], [1, 10, 107], [1, -10, 109], [1, -14, 113]], 'euler_factors_factorization': [[[[1, -1, 2], 1]], [1], [[[1, -1], 1]], [[[1, 4, 7], 1]], [[[1, 2, 11], 1]], [[[1, 1], 1]], [[[1, 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-0.489619506285701, -0.6646802585744758, -0.3460518228476164, 0.2428469783240832, 0.8080665754431727, 1.0974745491807634, 0.9920815388408847, 0.5431982121629085, -0.05717306944876584], 'positive_zeros': ['2.53409816778618263405222233424558', '3.51994456797006266949922249859162', '4.59731852050444182415870036677213', '5.66957165960173077695586779199567', '6.35831289645710659676663930684764', '7.36945570129601409328488904448187', '8.903866275348653436076253219749813', '9.238371497422229278947323218386275', '10.24076128195437772789084342069144'], 'prelabel': '2-585-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.161307131863703, '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': 854949074168896706, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.53409816778618263405222233425', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.51994456797006266949922249859', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.59731852050444182415870036677', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.671248518244905, 'bad_primes': [3, 5, 13], 'central_character': '1.1', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, -1, 1, 0, -4, -3, 0, 1, -2, 0, -1, -4, 0, -1, -2, 0, -6, -1, 0, -2, 6, 0, 1, -1, 0, 4, -2, 0, -10, 5, 0, -2, -4, 0, -2, -6, 0, -3, 6, 0, 10, 2, 0, 6, -4, 0, 9, 1, 0, 1, -2, 0, -2, 12, 0, -2, -6, 0, 2, -10, 0, 7, -1, 0, -4, 2, 0, -4, -6, 0, -6, -2, 0, 6, 8, 0, -12, -1, 0, 6, 16, 0, -2, 10, 0, 6, -2, 0, 4, -6, 0, -4, -6, 0, -2, 9, 0, -1], 'euler11': [1, 2, 11], 'euler13': [1, 1, 0], 'euler17': [1, 2, 17], 'euler19': [1, 6, 19], 'euler2': [1, -1, 2], 'euler23': [1, -6, 23], 'euler29': [1, 2, 29], 'euler3': [1, 0, 0], 'euler31': [1, 10, 31], 'euler37': [1, 2, 37], 'euler41': [1, -6, 41], 'euler43': [1, -10, 43], 'euler47': [1, 4, 47], 'euler5': [1, -1, 0], 'euler53': [1, 2, 53], 'euler59': [1, 6, 59], 'euler61': [1, -2, 61], 'euler67': [1, 4, 67], 'euler7': [1, 4, 7], 'euler71': [1, 6, 71], 'euler73': [1, 6, 73], 'euler79': [1, 12, 79], 'euler83': [1, -16, 83], 'euler89': [1, 2, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, -1, 2], [1, 0, 0], [1, -1, 0], [1, 4, 7], [1, 2, 11], [1, 1, 0], [1, 2, 17], [1, 6, 19], [1, -6, 23], [1, 2, 29], [1, 10, 31], [1, 2, 37], [1, -6, 41], [1, -10, 43], [1, 4, 47], [1, 2, 53], [1, 6, 59], [1, -2, 61], [1, 4, 67], [1, 6, 71], [1, 6, 73], [1, 12, 79], [1, -16, 83], [1, 2, 89], [1, 2, 97]], 'index': 18, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/585/h', 'ModularForm/GL2/Q/holomorphic/585/2/a/h/1/1', 'ModularForm/GL2/Q/holomorphic/585/2/a/h'], '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': '2-585-1.1-c1-0-18', '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': '2-585-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 854949074168896706, 'z1': {'__RealLiteral__': 0, 'data': '2.53409816778618263405222233425', 'prec': 103}}
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lfunc_instances • Show schema
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id: 11906862
{'Lhash': '3212351063431410795933612714663', 'Lhash_array': ['3212351063431410795933612714663'], 'label': '2-585-1.1-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/a/h'}
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id: 24549835
{'Lhash': '3212351063431410795933612714663', 'Lhash_array': ['3212351063431410795933612714663'], 'label': '2-585-1.1-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/a/h/1/1'}
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id: 96955
{'Lhash': '854949074168896706', 'Lhash_array': ['854949074168896706'], 'label': '2-585-1.1-c1-0-18', 'type': 'ECQ', 'url': 'EllipticCurve/Q/585/h'}