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lfunc_lfunctions • Show schema
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{'Lhash': '1242189141629498536099437325875', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.5, 0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [-1.5, 2.598076211353316], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 1.7320508075688772], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.2137261107234625, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-4.0, 1.7320508075688772]]]], 'bad_primes': [2, 19], 'central_character': '152.49', 'coefficient_field': 'CDF', 'conductor': 152, 'conductor_radical': 38, 'conjugate': '3529209908000873147749830220718', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.5, -0.8660254037844386], [-1.5, -2.598076211353316]], [[1.0, 0], [1.5, -2.598076211353316], [-2.5, -4.330127018922194]], [[1.0, 0], [0, 0], [7.0, 0]], [[1.0, 0], [4.0, 0], [11.0, 0]], [[1.0, 0], [-2.5, -4.330127018922194], [-6.5, 11.258330249197702]], [[1.0, 0], 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1.1568003694839362, 1.9172859996766576, 2.251256673460244, 2.0973145116436944, 1.527816123336567, 0.729616814189681], 'positive_zeros': ['0.979914450721557854737958164681696', '3.50875417154481424874690094536894', '5.03494778594923827488258126283417', '6.09566197658560200325766043446470', '7.78111380016531325454854692235580', '8.216548688067344586752233555431542', '9.656916818908247081094457171789042', '10.80376756342128163847906372350789', '12.01255057718805074530326390347798', '12.78901816022090662434005503767469'], 'prelabel': '2-152-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.101692384798707, 'root_angle': -0.5311600905421131, 'root_number': '-0.09773603764763142 - 0.995212372785297*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.265580045271', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.979914450721557854737958164682', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.50875417154481424874690094537', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.03494778594923827488258126283', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.2137261107234625, 'bad_primes': [2, 19], 'central_character': '19.11', 'conductor': 152, 'conductor_radical': 38, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/152/2/i/a/49/1'], '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': '2-152-19.11-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': '2-152-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.101692384798707, 'root_angle': -0.26558004527105655, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.979914450721557854737958164682', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1242189141629498536099437325875', 'Lhash_array': ['1242189141629498536099437325875'], 'label': '2-152-19.11-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/152/2/i/a/49/1'}