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lfunc_lfunctions • Show schema
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{'Lhash': '989703217585837372938402039226', 'a10': [8.196152422706632, -4.732050807568878], 'a2': [-1.3660254037844386, -0.36602540378443865], 'a3': [0.8660254037844386, 1.5], 'a4': [1.7320508075688772, 1.0], 'a5': [-4.732050807568878, 4.732050807568878], 'a6': [-0.6339745962155614, -2.366025403784439], 'a7': [-2.5, 0.6698729810778068], 'a8': [-2.0, -2.0], 'a9': [-1.5, 2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.125346062010316, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.3660254037844386, 0.36602540378443865]]], [3, [[1.0, 0], [-0.8660254037844386, -1.5]]], [13, [[1.0, 0], [-11.258330249197702, -6.5]]]], 'bad_primes': [2, 3, 13], 'central_character': '78.67', 'coefficient_field': 'CDF', 'conductor': 78, 'conductor_radical': 78, 'conjugate': '3523503474228320468721839463083', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.3660254037844386, 0.36602540378443865]], [[1.0, 0], 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'8.429120050449098872150162202723065', '8.791624177825614816892816836658070', '10.60517084826356908801010750901606', '11.66595961615128353447787153872655', '12.82314121002273354980699366142972', '13.72372676914253328030202378603820'], 'prelabel': '2-78-13.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4578566671694155, 'root_angle': -0.5751240971537339, 'root_number': '-0.23382443687416712 - 0.9722788348619333*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.287562048577', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.78073817612491168013945308798', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.45766718346058524052313076119', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.58411985960182780956895750200', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.125346062010316, 'bad_primes': [2, 3, 13], 'central_character': '13.2', 'conductor': 78, 'conductor_radical': 78, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/78/3/l/a/67/1'], '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': '2-78-13.2-c2-0-0', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-78-13.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4578566671694155, 'root_angle': -0.28756204857686696, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.78073817612491168013945308798', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '989703217585837372938402039226', 'Lhash_array': ['989703217585837372938402039226'], 'label': '2-78-13.2-c2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/78/3/l/a/67/1'}