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lfunc_lfunctions • Show schema
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{'Lhash': '2060456869612284545680585866822', 'a10': [0, 0], 'a2': [0, -2.0], 'a3': [0, -3.2601844233987607], 'a4': [-4.0, 0], 'a5': [0, 0], 'a6': [-6.520368846797521, 0], 'a7': [0, -27.792090452108656], 'a8': [0, 8.0], 'a9': [16.37119752542809, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 67.85219650660174, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 2.0]]], [5, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [0, -23.0]]]], 'bad_primes': [2, 5, 23], 'central_character': '1150.599', 'coefficient_field': 'CDF', 'conductor': 1150, 'conductor_radical': 230, 'conjugate': '369934833770841860496792995836', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.0]], [[1.0, 0], [0, 3.2601844233987607], [-27.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 27.792090452108656], [-343.0, 0]], [[1.0, 0], [10.818227889862362, 0], [1331.0, 0]], [[1.0, 0], [0, -36.96830513167439], [-2197.0, 0]], [[1.0, 0], [0, 118.99611612324044], [-4913.0, 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['1.62541387133119907854911041619841', '2.99126544011969767752453775946825', '4.03343516623480237186590536185804', '5.05615697864128135272055348086907', '5.71725585726902576200707517373109', '6.45411490972785111873474137133066', '7.65118843390306201679487151413854', '8.386129514893910103421364788732170', '9.025547234367822423554073144267747', '9.916354419504778235216396224946557'], 'prelabel': '2-1150-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.237244472917006, 'root_angle': -0.32379180882521663, 'root_number': '-0.4472135954999579392818347337462552470881236719223051449 - 0.8944271909999158785636694674925104941762473438446102897*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.32379180882521663', 'prec': 67}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.62541387133119907854911041620', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.99126544011969767752453775947', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.03343516623480237186590536186', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 67.85219650660174, 'bad_primes': [2, 5, 23], 'central_character': '5.4', 'conductor': 1150, 'conductor_radical': 230, 'degree': 2, 'index': 92, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1150/4/b/m/599/2'], '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': '2-1150-5.4-c3-0-92', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-1150-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.237244472917006, 'root_angle': -0.32379180882521663, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.62541387133119907854911041620', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2060456869612284545680585866822', 'Lhash_array': ['2060456869612284545680585866822'], 'factors': ['2-1150-5.4-c3-0-92'], 'label': '2-1150-5.4-c3-0-92', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1150/4/b/m/599/2'}