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lfunc_lfunctions • Show schema
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{'Lhash': '1069276577517617690891384388876', 'a10': [3.4061803330852602, -5.8996773966455525], 'a2': [-0.697597115419214, 2.603467877957997], 'a3': [0.0, 0.0], 'a4': [-4.55935244854903, -2.632343363500162], 'a5': [-2.441366411785082, -0.6541621584662805], 'a6': [0.0, 0.0], 'a7': [0.7221892148254158, 2.5452785187460036], 'a8': [6.222070981838351, -6.222070981838351], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.7221892148254158, -2.5452785187460036]]], [13, [[1.0, 0], [-1.4470273542679921, 3.302440285001407]]]], 'bad_primes': [3, 7, 13], 'central_character': '819.73', 'coefficient_field': 'CDF', 'conductor': 819, 'conductor_radical': 273, 'conjugate': '951481705947935364062513107601', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.697597115419214, -2.603467877957997], [-1.7320508075688772, -1.0]], 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'3.52277640947422917258568547351710', '4.05373637800564064335254020041303', '4.88079140570925287282109395881570', '6.90304780304506747830782640434358', '7.80427638125178558417593774953770', '8.409715963440527663095910296198388', '9.510599842114378937844422758723153', '10.14176219492156380737022315580881'], 'prelabel': '2-819-91.73-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': -0.28498964545633765, 'root_number': '-0.2180797482621401 - 0.9759309521671713*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.284989645456', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.843510488872173291962230562027', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.16547732264623979692051883387', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.52277640947422917258568547352', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'bad_primes': [3, 7, 13], 'central_character': '91.73', 'conductor': 819, 'conductor_radical': 273, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/819/2/fn/e/73/1'], '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': '2-819-91.73-c1-0-13', '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': '2-819-91.73-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': -0.28498964545633765, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.843510488872173291962230562027', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1069276577517617690891384388876', 'Lhash_array': ['1069276577517617690891384388876'], 'factors': ['2-819-91.73-c1-0-13'], 'label': '2-819-91.73-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/819/2/fn/e/73/1'}