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lfunc_lfunctions • Show schema
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{'Lhash': '1673232014899739122900945676561', 'a10': [-2.4751727510156045, -1.4290416540896858], 'a2': [0.25881904510252074, 0.9659258262890683], 'a3': [-1.4586457657319003, 0.9339981424566101], 'a4': [-0.8660254037844386, 0.5], 'a5': [-2.020970088409715, 2.020970088409715], 'a6': [-1.2796982317344217, -1.1672071091694887], 'a7': [3.467230655410537, 0.9290416540896858], 'a8': [-0.7071067811865476, -0.7071067811865476], 'a9': [1.255294939775204, -2.724744871391589], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6228331357659873, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.25881904510252074, -0.9659258262890683]]], [3, [[1.0, 0], [1.4586457657319003, -0.9339981424566101]]], [13, [[1.0, 0], [3.601205251626099, -0.1769766528686973]]]], 'bad_primes': [2, 3, 13], 'central_character': '78.59', 'coefficient_field': 'CDF', 'conductor': 78, 'conductor_radical': 78, 'conjugate': '4903995029174505950671303788585', 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['1.31994732191858571724124188622910', '4.33861600746475468326518792472316', '5.17896898050742297987606934606771', '7.23319642229864062345135020097690', '8.293483157278294185601681381058273', '9.868658593760215567117000642475067', '11.46646267030499352843651622908893', '11.75138188651280551331487761974496', '12.62466625153211681642075977431798', '13.95127112514186933297377284137484'], 'prelabel': '2-78-39.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7891977798790284, 'root_angle': -0.6217962338886119, 'root_number': '-0.3733654250306837 - 0.9276843533183348*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.310898116944', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.31994732191858571724124188623', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.33861600746475468326518792472', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.17896898050742297987606934607', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6228331357659873, 'bad_primes': [2, 3, 13], 'central_character': '39.20', 'conductor': 78, 'conductor_radical': 78, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/78/2/k/a/59/3'], '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': '2-78-39.20-c1-0-0', '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': '2-78-39.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7891977798790284, 'root_angle': -0.31089811694430597, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.31994732191858571724124188623', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1673232014899739122900945676561', 'Lhash_array': ['1673232014899739122900945676561'], 'label': '2-78-39.20-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/78/2/k/a/59/3'}