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lfunc_lfunctions • Show schema
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{'Lhash': '160256163956143712050489517037', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 1.0], 'a6': [0, 0], 'a7': [0, 3.414213562373095], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.498457891064382, '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, -1.0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1440.1151', 'coefficient_field': 'CDF', 'conductor': 1440, 'conductor_radical': 30, 'conjugate': '2705212214140924309092015413116', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, -3.414213562373095], [-7.0, 0]], [[1.0, 0], [2.585786437626905, 0], [11.0, 0]], [[1.0, 0], [3.414213562373095, 0], [13.0, 0]], [[1.0, 0], [0, 1.17157287525381], [-17.0, 0]], [[1.0, 0], [0, 0], [-19.0, 0]], [[1.0, 0], [4.82842712474619, 0], [23.0, 0]], [[1.0, 0], [0, 6.0], 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'6.79794682135626334160360276781102', '7.60277155322429224672156892572829', '8.100586217692038058966235330728081', '9.183930417254190500444321806524133'], 'prelabel': '2-1440-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.390937612381623, 'root_angle': 0.9459132760153036, 'root_number': '-0.98559855965348878087536279295293935430859299804623856409 + 0.1691019787257627481429347680509755569866105044940151880*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.47295663800765186', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.12641982256569041312251386921', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.59552567414014799363337751330', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.94443855828417120921757167260', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.498457891064382, 'bad_primes': [2, 3, 5], 'central_character': '12.11', 'conductor': 1440, 'conductor_radical': 30, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1440/2/h/a/1151/4'], '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': '2-1440-12.11-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': '2-1440-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.390937612381623, 'root_angle': 0.4729566380076518, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.12641982256569041312251386921', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '160256163956143712050489517037', 'Lhash_array': ['160256163956143712050489517037'], 'label': '2-1440-12.11-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1440/2/h/a/1151/4'}