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lfunc_lfunctions • Show schema
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{'Lhash': '753985043377997020058254264905,965185924620083502057222765454', 'a10': 4, 'a2': -2, 'a3': -2, 'a4': 3, 'a5': -2, 'a6': 4, 'a7': 3, 'a8': -4, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2355.459305720353, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2, 1]], [3, [1, 2, 1]], [1013, [1, -2, 1]]], 'bad_primes': [2, 3, 1013], 'central_character': '6078.1', 'coefficient_field': '1.1.1.1', 'conductor': 36942084, 'conductor_radical': 6078, 'degree': 4, 'euler_factors': [[1, 2, 1], [1, 2, 1], [1, 2, 6, 10, 25], [1, -3, 15, -21, 49], [1, -8, 38, -88, 121], [1, 8, 42, 104, 169], [1, -1, 23, -17, 289], [1, -9, 47, -171, 361], [1, -7, 57, -161, 529], [1, 12, 94, 348, 841], [1, 1, 1, 31, 961], [1, -5, 79, -185, 1369], [1, -9, 71, -369, 1681], [1, -5, 61, -215, 1849], [1, -20, 194, -940, 2209], [1, 7, 57, 371, 2809], [1, -15, 163, -885, 3481], [1, 21, 231, 1281, 3721], [1, -4, 58, -268, 4489], [1, -5, 137, -355, 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'7.948933351871451764592169890768004'], 'prelabel': '4-6078e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.966568333730335, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 225312165096915280, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.59478932384227058202086921098', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.76139744220237833636670332256', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.42529511940130741226743444596', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2355.459305720353, 'bad_primes': [2, 3, 1013], 'central_character': '1.1', 'conductor': 36942084, 'conductor_radical': 6078, 'degree': 4, 'dirichlet_coefficients': [1, -2, -2, 3, -2, 4, 3, -4, 3, 4, 8, -6, -8, -6, 4, 5, 1, -6, 9, -6, -6, -16, 7, 8, -2, 16, -4, 9, -12, -8, -1, -6, -16, -2, -6, 9, 5, -18, 16, 8, 9, 12, 5, 24, -6, -14, 20, -10, -6, 4, -2, -24, -7, 8, -16, -12, -18, 24, 15, 12, -21, 2, 9, 7, 16, 32, 4, 3, -14, 12, 5, -12, 1, -10, 4, 27, 24, -32, 0, -10, 5, -18, 6, -18, -2, -10, 24, -32, 10, 12, -24, 21, 2, -40, -18, 12, 11, 12, 24, -6], 'euler11': [1, -8, 38, -88, 121], 'euler13': [1, 8, 42, 104, 169], 'euler17': [1, -1, 23, -17, 289], 'euler19': [1, -9, 47, -171, 361], 'euler2': [1, 2, 1, 0, 0], 'euler23': [1, -7, 57, -161, 529], 'euler29': [1, 12, 94, 348, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, 1, 1, 31, 961], 'euler37': [1, -5, 79, -185, 1369], 'euler41': [1, -9, 71, -369, 1681], 'euler43': [1, -5, 61, -215, 1849], 'euler47': [1, -20, 194, -940, 2209], 'euler5': [1, 2, 6, 10, 25], 'euler53': [1, 7, 57, 371, 2809], 'euler59': [1, -15, 163, -885, 3481], 'euler61': [1, 21, 231, 1281, 3721], 'euler67': [1, -4, 58, -268, 4489], 'euler7': [1, -3, 15, -21, 49], 'euler71': [1, -5, 137, -355, 5041], 'euler73': [1, -1, 45, -73, 5329], 'euler79': [1, 0, 78, 0, 6241], 'euler83': [1, -6, 130, -498, 6889], 'euler89': [1, -10, 158, -890, 7921], 'euler97': [1, -11, 213, -1067, 9409], 'euler_factors': [[1, 2, 1, 0, 0], [1, 2, 1, 0, 0], [1, 2, 6, 10, 25], [1, -3, 15, -21, 49], [1, -8, 38, -88, 121], [1, 8, 42, 104, 169], [1, -1, 23, -17, 289], [1, -9, 47, -171, 361], [1, -7, 57, -161, 529], [1, 12, 94, 348, 841], [1, 1, 1, 31, 961], [1, -5, 79, -185, 1369], [1, -9, 71, -369, 1681], [1, -5, 61, -215, 1849], [1, -20, 194, -940, 2209], [1, 7, 57, 371, 2809], [1, -15, 163, -885, 3481], [1, 21, 231, 1281, 3721], [1, -4, 58, -268, 4489], [1, -5, 137, -355, 5041], [1, -1, 45, -73, 5329], [1, 0, 78, 0, 6241], [1, -6, 130, -498, 6889], [1, -10, 158, -890, 7921], [1, -11, 213, -1067, 9409]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6078/2/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': 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': '4-6078e2-1.1-c1e2-0-0', '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': 0, 'prelabel': '4-6078e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.966568333730335, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 225312165096915280, 'z1': {'__RealLiteral__': 0, 'data': '0.59478932384227058202086921098', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '753985043377997020058254264905,965185924620083502057222765454', 'Lhash_array': ['753985043377997020058254264905', '965185924620083502057222765454'], 'label': '4-6078e2-1.1-c1e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6078/2/a/c'}