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lfunc_lfunctions • Show schema
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{'Lhash': '731054027940149280524720854321,1181097298667032287184698252856', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 2, '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, -2, 6, -10, 25], [1, -2, 1], [1, -4, 26, -44, 121], [1, 0, 6, 0, 169], [1, 2, 30, 34, 289], [1, 2, 1], [1, 4, 50, 92, 529], [1, -2, 14, -58, 841], [1, 12, 78, 372, 961], [1, -8, 70, -296, 1369], [1, -8, 78, -328, 1681], [1, -16, 150, -688, 1849], [1, -10, 74, -470, 2209], [1, 18, 182, 954, 2809], [1, 0, 38, 0, 3481], [1, 0, -58, 0, 3721], [1, 12, 150, 804, 4489], [1, 2, 98, 142, 5041], [1, -16, 190, -1168, 5329], [1, -8, 174, 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3.138259609610352], 'positive_zeros': ['0.57669994224633301783839881853826', '0.931721484180566830078057361923423', '1.78316418100372479469732440228338', '1.79815819521805936961832817335600', '2.35648707723637607040628678586671', '2.55154079721994403318654530298217', '3.45695013805998129204336405156700', '3.54231726191946630869870498147666', '4.22674619226953325956924148818204', '4.25135340697210115009910119664539', '4.77012150595774402397662199076093', '4.99843751641245220274958892777995', '5.72162521374634430178265625180427', '5.90132473328886452694033131562515', '6.12148068225185191542316168771072', '6.24525672208393597435706760113002', '6.85702262341051165929962564897834', '7.25019596556098432038560281367414', '7.64437695385880725401287779005910', '7.67522543234814574563635983307230'], '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': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 2298131179184906345, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.57669994224633301783839881854', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.931721484180566830078057361923', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.78316418100372479469732440228', 'prec': 103}}
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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, 2, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, -4, 0, -2, 0, 0, 0, 2, 0, -12, 0, 0, 0, 4, 0, 8, 0, 0, 0, 8, 0, 16, 0, 0, 0, 10, 0, 3, 0, 0, 0, -18, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, -2, 0, 16, 0, 0, 0, 8, 0, 8, 0, 0, 0, 14, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -8, 0, 0, 0], 'euler11': [1, -4, 26, -44, 121], 'euler13': [1, 0, 6, 0, 169], 'euler17': [1, 2, 30, 34, 289], 'euler19': [1, 2, 1, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 4, 50, 92, 529], 'euler29': [1, -2, 14, -58, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 12, 78, 372, 961], 'euler37': [1, -8, 70, -296, 1369], 'euler41': [1, -8, 78, -328, 1681], 'euler43': [1, -16, 150, -688, 1849], 'euler47': [1, -10, 74, -470, 2209], 'euler5': [1, -2, 6, -10, 25], 'euler53': [1, 18, 182, 954, 2809], 'euler59': [1, 0, 38, 0, 3481], 'euler61': [1, 0, -58, 0, 3721], 'euler67': [1, 12, 150, 804, 4489], 'euler7': [1, -2, 1, 0, 0], 'euler71': [1, 2, 98, 142, 5041], 'euler73': [1, -16, 190, -1168, 5329], 'euler79': [1, -8, 174, -632, 6241], 'euler83': [1, -14, 170, -1162, 6889], 'euler89': [1, 0, 158, 0, 7921], 'euler97': [1, 8, 30, 776, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -2, 6, -10, 25], [1, -2, 1, 0, 0], [1, -4, 26, -44, 121], [1, 0, 6, 0, 169], [1, 2, 30, 34, 289], [1, 2, 1, 0, 0], [1, 4, 50, 92, 529], [1, -2, 14, -58, 841], [1, 12, 78, 372, 961], [1, -8, 70, -296, 1369], [1, -8, 78, -328, 1681], [1, -16, 150, -688, 1849], [1, -10, 74, -470, 2209], [1, 18, 182, 954, 2809], [1, 0, 38, 0, 3481], [1, 0, -58, 0, 3721], [1, 12, 150, 804, 4489], [1, 2, 98, 142, 5041], [1, -16, 190, -1168, 5329], [1, -8, 174, -632, 6241], [1, -14, 170, -1162, 6889], [1, 0, 158, 0, 7921], [1, 8, 30, 776, 9409]], 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9576/2/a/bv'], '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-c1e2-0-7', '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': '4-9576e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.744412214413165, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2298131179184906345, 'z1': {'__RealLiteral__': 0, 'data': '0.57669994224633301783839881854', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '731054027940149280524720854321,1181097298667032287184698252856', 'Lhash_array': ['731054027940149280524720854321', '1181097298667032287184698252856'], 'label': '4-9576e2-1.1-c1e2-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9576/2/a/bv'}