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lfunc_lfunctions • Show schema
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{'Lhash': '1259383272635575981604761983449', 'a10': [-2.980284590371443, -5.162004331537939], 'a2': [-1.3626251538627532, 2.360135998161647], 'a3': [0.6732080041229965, 1.1660304672030684], 'a4': [-2.7134946198789835, -4.699910547695198], 'a5': [-1.0935819663694628, 1.894139527992989], 'a6': [-3.669320640798941, -1.861316211831716e-60], 'a7': [-2.1972854742622236, 1.4737491457491112], 'a8': [9.3394034802224, 0.0], 'a9': [0.5935819663694629, -1.0281141242085503], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [2.1972854742622236, -1.4737491457491112]]], [13, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [7, 13], 'central_character': '91.79', 'coefficient_field': 'CDF', 'conductor': 91, 'conductor_radical': 91, 'conjugate': '4914622021967380170457409809360', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.3626251538627532, -2.360135998161647], [-1.0, 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'7.32413325198305120609787608017227', '8.247696078859357709374601878555647', '9.249721370492210665286032368310786', '10.24256660250354645450775585500874', '11.44037309003357323367744244200425', '12.41064474962399888595216686623144', '13.11111984404735146069596187764884'], 'prelabel': '2-91-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': 0.9584365310942283, 'root_number': '-0.9914871265550291 + 0.1302047536599631*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.479218265547', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.993478228471500774835515713466', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.92050571152363376177525191301', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.37162808524744484568853269875', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'bad_primes': [7, 13], 'central_character': '7.2', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/91/2/e/c/79/1'], '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': '2-91-7.2-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': '2-91-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': 0.47921826554711416, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.993478228471500774835515713466', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1259383272635575981604761983449', 'Lhash_array': ['1259383272635575981604761983449'], 'label': '2-91-7.2-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/2/e/c/79/1'}