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lfunc_lfunctions • Show schema
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{'Lhash': '700491439757092257842745850248', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [2.6281389727906896, 2.6281389727906896], 'a6': [0, 0], 'a7': [-1.0, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.19568209498026, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '4032.1583', 'coefficient_field': 'CDF', 'conductor': 4032, 'conductor_radical': 42, 'conjugate': '1835301072857312215852017410153', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.6281389727906896, -2.6281389727906896], [0, 5.0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0.5831400789295093, -0.5831400789295093], [0, -11.0]], [[1.0, 0], [-1.765903467988989, -1.765903467988989], [0, 13.0]], [[1.0, 0], [0, -3.637344141916484], [-17.0, 0]], [[1.0, 0], 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1.3567059863099042, 1.1314715663888217, 0.8745861233540119, 0.6090154331178584], 'positive_zeros': ['0.55259031126634965646649789605304', '1.55516672340730209524291635303069', '2.54998065217202724531291885354050', '3.52339006359626117132764067691217', '4.63205241210495554714297682760673', '5.30682986341590788770956703904775', '5.83344181637536387718876054895026', '6.60604113229231971906625781369466', '7.51769878037057420070361925109178', '8.399879814358693862379565981783634'], 'prelabel': '2-4032-48.35-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.674123905501206, 'root_angle': -0.6429114692726412, 'root_number': '-0.43403750247671628677335077368074769090732909180650737618 - 0.90089480320610935535756381514102247515017039305625194508*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3214557346363206', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.55259031126634965646649789605', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.55516672340730209524291635303', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.54998065217202724531291885354', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.19568209498026, 'bad_primes': [2, 3, 7], 'central_character': '48.35', 'conductor': 4032, 'conductor_radical': 42, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4032/2/v/e/1583/19'], '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': '2-4032-48.35-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': '2-4032-48.35-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.674123905501206, 'root_angle': -0.3214557346363206, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.55259031126634965646649789605', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '700491439757092257842745850248', 'Lhash_array': ['700491439757092257842745850248'], 'label': '2-4032-48.35-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4032/2/v/e/1583/19'}