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lfunc_lfunctions • Show schema
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{'Lhash': '2514012162096062121925303580814', 'a10': [0, 0], 'a2': [0, 0], 'a3': [2.498936669825207, 0], 'a4': [0, 0], 'a5': [2.1967566331198296, -0.41744496025707395], 'a6': [0, 0], 'a7': [0, -3.0492181092094772], 'a8': [0, 0], 'a9': [3.2446844797970953, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.692473971915598, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-2.1967566331198296, 0.41744496025707395]]], [23, [[1.0, 0], [-3.791272651379697, 2.9370481240354853]]]], 'bad_primes': [2, 5, 23], 'central_character': '1840.1839', 'coefficient_field': 'CDF', 'conductor': 1840, 'conductor_radical': 230, 'conjugate': '1123241609656003284005036793853', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.498936669825207, 0], [3.0, 0]], [[1.0, 0], [-2.1967566331198296, 0.41744496025707395]], [[1.0, 0], [0, 3.0492181092094772], [-7.0, 0]], [[1.0, 0], [5.879617365978553, 0], 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-0.42429631886015157], 'positive_zeros': ['1.98320590992773262921010921872280', '2.35390132001558371894290997681598', '3.14493504179343757079454099625604', '4.42209183447678658405829168813306', '5.46038758666877787685675817314978', '6.11188441107172247804517448195708', '7.29791965689786081028793159375377', '7.895370778800605081134734295039814', '8.927109314650822970292928644885266', '9.169360639876920588688815084916607'], 'prelabel': '2-1840-460.459-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.833076306560515, 'root_angle': 0.39708904502871406, 'root_number': '0.31770139632633838759154907674503645975269584172120142796 + 0.94819081559161648593434474019136471022200071481890860018*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.19854452251435703', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.98320590992773262921010921872', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.35390132001558371894290997682', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.14493504179343757079454099626', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.692473971915598, 'bad_primes': [2, 5, 23], 'central_character': '460.459', 'conductor': 1840, 'conductor_radical': 230, 'degree': 2, 'index': 67, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1840/2/m/g/1839/34'], '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': '2-1840-460.459-c1-0-67', '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': '2-1840-460.459-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.833076306560515, 'root_angle': 0.19854452251435703, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.98320590992773262921010921872', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2514012162096062121925303580814', 'Lhash_array': ['2514012162096062121925303580814'], 'label': '2-1840-460.459-c1-0-67', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1840/2/m/g/1839/34'}