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lfunc_lfunctions • Show schema
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{'Lhash': '1177180487417861673516079659659', 'a10': [2.414213562373095, -2.414213562373095], 'a2': [0, -1.0], 'a3': [0.7071067811865476, 0.7071067811865476], 'a4': [-1.0, 0], 'a5': [2.414213562373095, 2.414213562373095], 'a6': [0.7071067811865476, -0.7071067811865476], 'a7': [0, 0], 'a8': [0, 1.0], 'a9': [0, 1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.959215106787664, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.0]]], [3, [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]]], [11, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [17, [[1.0, 0], [1.0, -4.0]]]], 'bad_primes': [2, 3, 11, 17], 'central_character': '1122.727', 'coefficient_field': 'CDF', 'conductor': 1122, 'conductor_radical': 1122, 'conjugate': '2141043058573074155368622116668', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0]], [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [-2.414213562373095, 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2.6836322559324817, 2.9288693212855788, 3.075316470497116, 3.1080244123971106, 3.018527983928969, 2.8055915278428607, 2.4754903084087405, 2.041801478504615, 1.524710618311189, 0.949872423221613, 0.3468945393071554], 'positive_zeros': ['0.928631664912966257754389363238247', '2.14966229271506686751957181612865', '3.58767000637891339174228522269152', '4.86070657285716384491230213780711', '5.54086418008100514368051642594464', '6.33698559939816904732372530848243', '7.24746381529542491808345652236549', '8.221756821614395793691860248230011', '8.882750834296987774179392726442177', '9.391599515315582539829544033073235'], 'prelabel': '2-1122-17.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9931947993386037, 'root_angle': -0.21101043481131532, 'root_number': '0.78820543801610915221774562678980564844118720975331186164 - 0.61541220940263568453061943924198163983592820489629661801*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.10550521740565769', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.928631664912966257754389363238', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.14966229271506686751957181613', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.58767000637891339174228522269', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.959215106787664, 'bad_primes': [2, 3, 11, 17], 'central_character': '17.13', 'conductor': 1122, 'conductor_radical': 1122, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1122/2/l/c/727/2'], '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': '2-1122-17.13-c1-0-13', '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': '2-1122-17.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9931947993386037, 'root_angle': -0.10550521740565766, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.928631664912966257754389363238', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1177180487417861673516079659659', 'Lhash_array': ['1177180487417861673516079659659'], 'label': '2-1122-17.13-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1122/2/l/c/727/2'}