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lfunc_lfunctions • Show schema
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{'Lhash': '900378042374346214153350373096', 'a10': [0.0, 0.0], 'a2': [-0.2225209339563144, -0.9749279121818236], 'a3': [0.2225209339563144, 0.9749279121818236], 'a4': [-0.9009688679024191, 0.4338837391175581], 'a5': [0.0, 0.0], 'a6': [0.9009688679024191, -0.4338837391175581], 'a7': [0.0, 0.0], 'a8': [0.6234898018587335, 0.7818314824680298], 'a9': [-0.9009688679024191, 0.4338837391175581], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5150350930372585, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.2225209339563144, 0.9749279121818236]]], [3, [[1.0, 0], [-0.2225209339563144, -0.9749279121818236]]], [43, [[1.0, 0], [-0.2225209339563144, -0.9749279121818236]]]], 'bad_primes': [2, 3, 43], 'central_character': '1032.371', 'coefficient_field': 'CDF', 'conductor': 1032, 'conductor_radical': 258, 'conjugate': '2542298637812555556499674739441', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.2225209339563144, 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'2.50963545228650022668822852925059', '3.75815495996373369189975912752102', '5.17327599026101054382925913457606', '5.96868260799295179570119997607871', '6.61014690145896450058453425822338', '7.53865475268469011225255330976097', '8.375246232920054217936101233283257', '8.645548679554119015281520359451424', '9.733204993555613134951521996641282'], 'prelabel': '2-1032-1032.371-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7176594547814851, 'root_angle': -0.3484972401188785, 'root_number': '0.45819191949043289111595674393530 - 0.88885328649539945531110879807209*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.17424862005943925', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.71027303754854927997856788619', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.50963545228650022668822852925', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.75815495996373369189975912752', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5150350930372585, 'bad_primes': [2, 3, 43], 'central_character': '1032.371', 'conductor': 1032, 'conductor_radical': 258, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1032/1/bv/a/371/1'], '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': '2-1032-1032.371-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1032-1032.371-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7176594547814851, 'root_angle': -0.17424862005943925, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.71027303754854927997856788619', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '900378042374346214153350373096', 'Lhash_array': ['900378042374346214153350373096'], 'label': '2-1032-1032.371-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1032/1/bv/a/371/1'}