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lfunc_lfunctions • Show schema
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{'Lhash': '1476683935559084503447759951384,1761352543551705588028858025777', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5846.857224180202, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, -2, 1]], [19, [1, -2, 1]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '9576.1', 'coefficient_field': '1.1.1.1', 'conductor': 91699776, 'conductor_radical': 798, 'degree': 4, 'euler_factors': [[1], [1], [1, 0, 5, 0, 25], [1, -2, 1], [1, -1, 11, -11, 121], [1, 8, 37, 104, 169], [1, -5, 29, -85, 289], [1, -2, 1], [1, 8, 57, 184, 529], [1, -11, 87, -319, 841], [1, 7, 73, 217, 961], [1, 6, 63, 222, 1369], [1, -1, -19, -41, 1681], [1, -4, 10, -172, 1849], [1, 14, 143, 658, 2209], [1, 3, 97, 159, 2809], [1, -8, 89, -472, 3481], [1, 12, 113, 732, 3721], [1, 9, 153, 603, 4489], [1, -10, 87, -710, 5041], [1, 7, 147, 511, 5329], [1, 0, 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'positive_zeros': ['1.16489822613046566498168544388994', '1.38946216191953009008290482688353', '2.14026425352790572523620344995134', '2.22674714033674305834178525694355', '2.77597498803856012760135702108507', '3.24345913038008350756599188491718', '3.73810308657856849559519622533476', '3.87566691652684810545411004986360', '4.63210974278375669656928876544307', '4.72229861920770328497778172300527', '5.10069711268777047485355102370130', '5.31188770468733093912461425437440', '5.96909335183284681638111578499204', '5.98535997228150715919125209528804', '6.52492701833764503946545740075807', '6.90701745794455051420361863498981', '7.35618368413859942922014567116276', '7.49518463384154262959322128697524'], 'prelabel': '4-9576e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.744412214413165, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5846.857224180202, 'bad_primes': [2, 3, 7, 19], 'central_character': '1.1', 'conductor': 91699776, 'conductor_radical': 798, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, -8, 0, 0, 0, 5, 0, 2, 0, 0, 0, -8, 0, -5, 0, 0, 0, 11, 0, -7, 0, 0, 0, 0, 0, -6, 0, 0, 0, 1, 0, 4, 0, 0, 0, -14, 0, 3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 8, 0, -12, 0, 0, 0, 0, 0, -9, 0, 0, 0, 10, 0, -7, 0, 0, 0, 2, 0, 0, 0, 0, 0, 25, 0, 0, 0, 0, 0, -6, 0, -16, 0, 0, 0, 0, 0, -12, 0, 0, 0], 'euler11': [1, -1, 11, -11, 121], 'euler13': [1, 8, 37, 104, 169], 'euler17': [1, -5, 29, -85, 289], 'euler19': [1, -2, 1, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 8, 57, 184, 529], 'euler29': [1, -11, 87, -319, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 7, 73, 217, 961], 'euler37': [1, 6, 63, 222, 1369], 'euler41': [1, -1, -19, -41, 1681], 'euler43': [1, -4, 10, -172, 1849], 'euler47': [1, 14, 143, 658, 2209], 'euler5': [1, 0, 5, 0, 25], 'euler53': [1, 3, 97, 159, 2809], 'euler59': [1, -8, 89, -472, 3481], 'euler61': [1, 12, 113, 732, 3721], 'euler67': [1, 9, 153, 603, 4489], 'euler7': [1, -2, 1, 0, 0], 'euler71': [1, -10, 87, -710, 5041], 'euler73': [1, 7, 147, 511, 5329], 'euler79': [1, 0, 138, 0, 6241], 'euler83': [1, -25, 321, -2075, 6889], 'euler89': [1, 6, 182, 534, 7921], 'euler97': [1, 12, 225, 1164, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, 5, 0, 25], [1, -2, 1, 0, 0], [1, -1, 11, -11, 121], [1, 8, 37, 104, 169], [1, -5, 29, -85, 289], [1, -2, 1, 0, 0], [1, 8, 57, 184, 529], [1, -11, 87, -319, 841], [1, 7, 73, 217, 961], [1, 6, 63, 222, 1369], [1, -1, -19, -41, 1681], [1, -4, 10, -172, 1849], [1, 14, 143, 658, 2209], [1, 3, 97, 159, 2809], [1, -8, 89, -472, 3481], [1, 12, 113, 732, 3721], [1, 9, 153, 603, 4489], [1, -10, 87, -710, 5041], [1, 7, 147, 511, 5329], [1, 0, 138, 0, 6241], [1, -25, 321, -2075, 6889], [1, 6, 182, 534, 7921], [1, 12, 225, 1164, 9409]], 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9576/2/a/bm'], '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': '4-9576e2-1.1-c1e2-0-18', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'prelabel': '4-9576e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.744412214413165, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 7361725736948928, 'z1': {'__RealLiteral__': 0, 'data': '1.16489822613046566498168544389', 'prec': 103}}
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{'Lhash': '1476683935559084503447759951384,1761352543551705588028858025777', 'Lhash_array': ['1476683935559084503447759951384', '1761352543551705588028858025777'], 'label': '4-9576e2-1.1-c1e2-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9576/2/a/bm'}