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lfunc_lfunctions • Show schema
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{'Lhash': '2426922870577882210082412749084', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0.5, -0.8660254037844386], 'a4': [0, 0], 'a5': [-1.849814074137659, -3.203971960962407], 'a6': [0, 0], 'a7': [1.2385499165474452, 2.3379465571779687], 'a8': [0, 0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.719663900723821, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.5, 0.8660254037844386]]], [7, [[1.0, 0], [-1.2385499165474452, -2.3379465571779687]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '1092.781', 'coefficient_field': 'CDF', 'conductor': 1092, 'conductor_radical': 546, 'conjugate': '557839369210710263526124562121', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [1.849814074137659, 3.203971960962407], [-2.5, 4.330127018922194]], [[1.0, 0], [-1.2385499165474452, 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'9.724322675816064132337184072547072', '10.26110198602479264725152346531215'], 'prelabel': '2-1092-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9529077027099615, 'root_angle': 0.4325508077218918, 'root_number': '-0.91153459970365259984291364187771498091523291130876416753 + 0.4112233864253124133579149979285339481109984269473208376*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4325508077218918', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.91450457258564463845044485771', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.33606832348115390286950231810', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.85815287957066482884080029611', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.719663900723821, 'bad_primes': [2, 3, 7, 13], 'central_character': '7.4', 'conductor': 1092, 'conductor_radical': 546, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1092/2/q/d/781/1'], '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': '2-1092-7.4-c1-0-14', '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': '2-1092-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9529077027099615, 'root_angle': 0.4325508077218918, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.91450457258564463845044485771', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2426922870577882210082412749084', 'Lhash_array': ['2426922870577882210082412749084'], 'factors': ['2-1092-7.4-c1-0-14'], 'label': '2-1092-7.4-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1092/2/q/d/781/1'}