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lfunc_lfunctions • Show schema
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{'Lhash': '3108503795074268170581158425693', 'a10': [0.3722813232690143, 1.7320508075688772], 'a2': [0.0, -0.7922869913932613], 'a3': [0.0, 2.5243377989621387], 'a4': [1.3722813232690143, 0.0], 'a5': [-2.186140661634507, 0.469881908087808], 'a6': [2.0, 0.0], 'a7': [0.0, -3.4641016151377544], 'a8': [0.0, -2.6718146237444933], 'a9': [-3.3722813232690143, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.43917721111704233, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [2.186140661634507, -0.469881908087808]]], [11, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [5, 11], 'central_character': '55.34', 'coefficient_field': 'CDF', 'conductor': 55, 'conductor_radical': 55, 'conjugate': '4411222022837444108696624694432', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0.7922869913932613], [-2.0, 0]], [[1.0, 0], [0, -2.5243377989621387], [-3.0, 0]], [[1.0, 0], [2.186140661634507, -0.469881908087808]], [[1.0, 0], [0, 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'5.52923801730463138407263999870173', '6.85437210822826851515912330194396', '7.75464132179680785468636652988306', '8.752358483478454298537765325142651', '11.23905208913192929239537573227480', '12.04501127844926345527565061308016', '12.77160542675294909516894765829353', '14.32625908956387078472543558768188', '15.45163900919693144083861587179257'], 'prelabel': '2-55-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6627044674038665, 'root_angle': -0.06739119311870337, 'root_number': '0.977671825558225 - 0.21013757757632937*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0336955965594', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.45217711766523776713592093680', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.52923801730463138407263999870', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.85437210822826851515912330194', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.43917721111704233, 'bad_primes': [5, 11], 'central_character': '5.4', 'conductor': 55, 'conductor_radical': 55, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/55/2/b/a/34/2'], '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': '2-55-5.4-c1-0-1', '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': '2-55-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6627044674038665, 'root_angle': -0.033695596559351684, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.45217711766523776713592093680', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3108503795074268170581158425693', 'Lhash_array': ['3108503795074268170581158425693'], 'label': '2-55-5.4-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/55/2/b/a/34/2'}