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lfunc_lfunctions • Show schema
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{'Lhash': '1399405180978885578604110131189', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-0.7399209796112353, -1.7863272640618304], 'a6': [0, 0], 'a7': [-0.3854165715498347, -0.3854165715498347], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.198766312851504, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1152.1007', 'coefficient_field': 'CDF', 'conductor': 1152, 'conductor_radical': 6, 'conjugate': '1128406454600740293312229263666', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.7399209796112353, 1.7863272640618304], [-3.5355339059327378, 3.5355339059327378]], [[1.0, 0], [0.3854165715498347, 0.3854165715498347], [0, 7.0]], [[1.0, 0], [-2.363982038706787, -5.707157499052324], [-7.7781745930520225, 7.7781745930520225]], [[1.0, 0], [2.309159674988937, 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'9.103870427595146562912312532182787', '9.849533473971508412282610184918007'], 'prelabel': '2-1152-96.83-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.032946803498456, 'root_angle': 0.17582542651765384, 'root_number': '0.8512823799249402096654396985099568115822468478441713232 + 0.5247078326357724135388648491431527662905131396369431240*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.08791271325882692', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.10393603783797752897975721084', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.94232629292965474215017637939', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.38363964041764555618344809539', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.198766312851504, 'bad_primes': [2, 3], 'central_character': '96.83', 'conductor': 1152, 'conductor_radical': 6, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1152/2/w/b/1007/3'], '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': '2-1152-96.83-c1-0-8', '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': '2-1152-96.83-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.032946803498456, 'root_angle': 0.08791271325882692, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.10393603783797752897975721084', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1399405180978885578604110131189', 'Lhash_array': ['1399405180978885578604110131189'], 'label': '2-1152-96.83-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1152/2/w/b/1007/3'}