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lfunc_lfunctions • Show schema
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{'Lhash': '3540718574285699032266457644788', 'a10': [-1.4951513219603334, -0.6656842574137192], 'a2': [2.1763815357082117, -1.5812337428576335], 'a3': [1.2964710401708335, -0.5772260967558506], 'a4': [1.6183024506701773, -4.980622810597972], 'a5': [-0.3041918701007916, -0.526875774263963], 'a6': [1.9088862519598646, -3.306287974264211], 'a7': [-1.1555076007713008, -1.2833212023968614], 'a8': [-2.690877727428328, -8.281670082257724], 'a9': [-0.6597446278509265, 0.7327206402825673], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.673623634245049, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[31, [[1.0, 0], [0, 0]]]], 'bad_primes': [31], 'central_character': '961.235', 'coefficient_field': 'CDF', 'conductor': 961, 'conductor_radical': 31, 'conjugate': '1598729180388074779303326053183', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.1763815357082117, 1.5812337428576335], [0.6180339887498949, -1.902113032590307]], [[1.0, 0], 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'data': '0.40271203343', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.79313445964386687170906588628', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.20299359259054561230143368856', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.13049743937570584655639856599', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.673623634245049, 'bad_primes': [31], 'central_character': '31.18', 'conductor': 961, 'conductor_radical': 31, 'degree': 2, 'index': 62, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/961/2/g/s/235/2'], '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': '2-31e2-31.18-c1-0-62', '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': '2-31e2-31.18-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.77013061682027, 'root_angle': 0.4027120334298637, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.79313445964386687170906588628', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3540718574285699032266457644788', 'Lhash_array': ['3540718574285699032266457644788'], 'label': '2-31e2-31.18-c1-0-62', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/961/2/g/s/235/2'}