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lfunc_lfunctions • Show schema
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{'Lhash': '1052425039824640433446219149685', 'a10': [-2.2359665682776417, 0.021295669623332566], 'a2': [-0.5, 0.8660254037844386], 'a3': [0.533793382171979, 0.9245572586658987], 'a4': [-0.5, -0.8660254037844386], 'a5': [1.1364258750232274, 1.925756015329484], 'a6': [-1.067586764343958, -3.325136716092755e-61], 'a7': [1.2210675077887796, 2.3471246540016786], 'a8': [1.0, 0.0], 'a9': [0.9301292502987991, -1.6110311191234694], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.148480955638592, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, -0.8660254037844386]]], [5, [[1.0, 0], [-1.1364258750232274, -1.925756015329484]]], [7, [[1.0, 0], [-1.2210675077887796, -2.3471246540016786]]], [11, [[1.0, 0], [2.752058327859928, -1.8509929659663265]]]], 'bad_primes': [2, 5, 7, 11], 'central_character': '770.439', 'coefficient_field': 'CDF', 'conductor': 770, 'conductor_radical': 770, 'conjugate': 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'3.10851442394123760335599118547669', '4.58688874018367141265189256535383', '5.20546722208826897236221975401261', '6.67463357257568837635774842678148', '7.74239484902805277202583680304911', '8.246516957838494741717718139746232', '9.031967340409683125688161985301429', '10.25513839899096579415801627891433'], 'prelabel': '2-770-385.54-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4796130657097675, 'root_angle': -0.8038491053873347, 'root_number': '-0.8160653610050683 - 0.5779596236482853*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.401924552694', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.830216969593325251740130824635', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.90710785363511210301800814881', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.10851442394123760335599118548', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.148480955638592, 'bad_primes': [2, 5, 7, 11], 'central_character': '385.54', 'conductor': 770, 'conductor_radical': 770, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/770/2/o/a/439/15'], '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': '2-770-385.54-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': '2-770-385.54-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4796130657097675, 'root_angle': -0.40192455269366734, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.830216969593325251740130824635', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1052425039824640433446219149685', 'Lhash_array': ['1052425039824640433446219149685'], 'label': '2-770-385.54-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/770/2/o/a/439/15'}