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lfunc_lfunctions • Show schema
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{'Lhash': '805534957870447292562201775686', 'a10': [0.0, 0.0], 'a2': [-1.4416788403346845, -1.0474409892285987], 'a3': [0.0, 0.0], 'a4': [0.6722882583776278, 2.0690905050450485], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.9510565162951535, 0.30901699437494745], 'a8': [0.6473541325530865, -1.9923511564810013], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.3458520537546707, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.9510565162951535, -0.30901699437494745]]], [11, [[1.0, 0], [0.15643446504023087, -0.9876883405951378]]]], 'bad_primes': [3, 7, 11], 'central_character': '693.62', 'coefficient_field': 'CDF', 'conductor': 693, 'conductor_radical': 231, 'conjugate': '1999199930103375073742197722173', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.4416788403346845, 1.0474409892285987], [0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], 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'9.593077544384556870978776908901982', '10.31458672137530169813646691655350'], 'prelabel': '2-693-231.62-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5880918752666718, 'root_angle': -0.13195350991956648, 'root_number': '0.91530000851041101195949647625606 - 0.40277275779382290427564264820825*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.06597675495978324', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.63545503605285065932662652634', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.63805802925140126106760694773', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.26312641794211840402204527469', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.3458520537546707, 'bad_primes': [3, 7, 11], 'central_character': '231.62', 'conductor': 693, 'conductor_radical': 231, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/693/1/bp/a/62/1'], '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': '2-693-231.62-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-693-231.62-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5880918752666718, 'root_angle': -0.06597675495978324, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.63545503605285065932662652634', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '805534957870447292562201775686', 'Lhash_array': ['805534957870447292562201775686'], 'label': '2-693-231.62-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/693/1/bp/a/62/1'}