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lfunc_lfunctions • Show schema
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{'Lhash': '186597083133959782808103109742', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0.5, -0.8660254037844386], 'a6': [0, 0], 'a7': [-1.3228756555322954, 2.29128784747792], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.061150654681333, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.5, 0.8660254037844386]]], [7, [[1.0, 0], [1.3228756555322954, -2.29128784747792]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1260.541', 'coefficient_field': 'CDF', 'conductor': 1260, 'conductor_radical': 210, 'conjugate': '2278288168844431148026014709445', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [1.3228756555322954, -2.29128784747792]], [[1.0, 0], [0.8228756555322952, 1.4252624436934813], [-5.5, 9.526279441628825]], [[1.0, 0], 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'root_analytic_conductor': 3.1719316913643225, 'root_angle': -0.8535062863872795, 'root_number': '-0.8959532196631047777472502077045651416017253591988638480 - 0.4441484303420606689180796704892532333801192844401406236*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4267531431936398', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.14719914391265590872760251820', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.99080297305571502335173203087', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.04959555633982764802269314723', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.061150654681333, 'bad_primes': [2, 3, 5, 7], 'central_character': '7.2', 'conductor': 1260, 'conductor_radical': 210, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1260/2/s/f/541/1'], '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': '2-1260-7.2-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': '2-1260-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1719316913643225, 'root_angle': -0.4267531431936398, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.14719914391265590872760251820', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '186597083133959782808103109742', 'Lhash_array': ['186597083133959782808103109742'], 'label': '2-1260-7.2-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1260/2/s/f/541/1'}