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lfunc_lfunctions • Show schema
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{'Lhash': '1762906835619174968442842902259', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [3.0, 0.0], 'a4': [0.0, 0.0], 'a5': [5.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-35.1436238221232, 0.0], 'a8': [0.0, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 92.0429796089554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-3.0, 0]]], [5, [[1.0, 0], [-5.0, 0]]], [13, [[1.0, 0], [-13.0, 0]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1560.1', 'coefficient_field': 'CDF', 'conductor': 1560, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [-5.0, 0]], [[1.0, 0], [35.1436238221232, 0], [343.0, 0]], [[1.0, 0], [-13.743964964815794, 0], [1331.0, 0]], [[1.0, 0], [-13.0, 0]], [[1.0, 0], [-87.15774616533704, 0], [4913.0, 0]], [[1.0, 0], [-11.686906501553821, 0], [6859.0, 0]], [[1.0, 0], [108.26183399761955, 0], 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'5.74327854640301010346055229222363', '6.08772275309199311849767752079394', '7.11685355185143371520641982526657', '7.77914174161419444044131370656515', '8.983770738720466213523883455099643'], 'prelabel': '2-1560-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.593903252011426, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.39068828216685182347203874719', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.68310646449846113402485127350', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.41179852419118532223301766889', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 92.0429796089554, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 1560, 'conductor_radical': 390, 'degree': 2, 'index': 59, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1560/4/a/n/1/1'], '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': '2-1560-1.1-c3-0-59', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-1560-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.593903252011426, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.39068828216685182347203874719', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1762906835619174968442842902259', 'Lhash_array': ['1762906835619174968442842902259'], 'label': '2-1560-1.1-c3-0-59', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1560/4/a/n/1/1'}