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lfunc_lfunctions • Show schema
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{'Lhash': '1331848428490537408085231766418', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [2.0907702751760278, 3.6213203435596424], 'a6': [0, 0], 'a7': [1.6213203435596426, 2.0907702751760278], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.048920523745066, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.6213203435596426, -2.0907702751760278]]]], 'bad_primes': [2, 3, 7], 'central_character': '1008.17', 'coefficient_field': 'CDF', 'conductor': 1008, 'conductor_radical': 42, 'conjugate': '2321941671509073296843685077763', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.0907702751760278, -3.6213203435596424], [-2.5, 4.330127018922194]], [[1.0, 0], [-1.6213203435596426, -2.0907702751760278]], [[1.0, 0], [-2.598076211353316, -1.5], [5.5, 9.526279441628825]], [[1.0, 0], [0, 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2.837061952750603, 'root_angle': -0.22310832912105213, 'root_number': '0.16816252474781325110594438542950921818629161607839870119 - 0.98575928363391084822565631342742146204357394025126429135*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.22310832912105213', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.05064315691622734939393738901', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.79591602732710900154590549549', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.64749594222050520309198451140', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.048920523745066, 'bad_primes': [2, 3, 7], 'central_character': '21.17', 'conductor': 1008, 'conductor_radical': 42, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1008/2/bt/c/17/4'], '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': '2-1008-21.17-c1-0-7', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1008-21.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.837061952750603, 'root_angle': -0.22310832912105213, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.05064315691622734939393738901', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1331848428490537408085231766418', 'Lhash_array': ['1331848428490537408085231766418'], 'factors': ['2-1008-21.17-c1-0-7'], 'label': '2-1008-21.17-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1008/2/bt/c/17/4'}