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lfunc_lfunctions • Show schema
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{'Lhash': '2499191152774221618693292006978', 'a10': [7.5706377253761366, 0.0], 'a2': [2.457789457497516, 0.0], 'a3': [0.0, 0.0], 'a4': [4.040729017385934, 0.0], 'a5': [3.0802629176725516, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.658667133598251, 0.0], 'a8': [5.015682264540414, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.1', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '2499191152774221618693292006978', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.457789457497516, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.0802629176725516, 0], [5.0, 0]], [[1.0, 0], [2.658667133598251, 0], [7.0, 0]], [[1.0, 0], [-3.4343407024075385, 0], [11.0, 0]], [[1.0, 0], [3.343956128470459, 0], [13.0, 0]], [[1.0, 0], [2.5728179036238905, 0], [17.0, 0]], 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'4.96916465618776219066087924015689', '5.95935953697554333580735664585285', '6.44919069617124175684135911984073', '7.14905099169695093529453024670835', '8.912867490282402835491836840994816', '9.701782845455050464096387885269092', '10.45993401100749620352636241799873'], 'prelabel': '2-3e6-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.97151419509781647553660511517', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.86788501803561593153001593501', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.00043091038429119732600511879', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '1.1', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/a/b/1/6'], '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': '2-3e6-1.1-c1-0-24', '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': '2-3e6-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.97151419509781647553660511517', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2499191152774221618693292006978', 'Lhash_array': ['2499191152774221618693292006978'], 'label': '2-3e6-1.1-c1-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/a/b/1/6'}