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  • lfunc_lfunctions • Show schema
    {'Lhash': '2184784845462951857781015507118', 'a10': [-1.1847925309040954, 0.0], 'a2': [-1.0, 0.0], 'a3': [3.2266815969056775, 0.0], 'a4': [1.0, 0.0], 'a5': [1.1847925309040954, 0.0], 'a6': [-3.2266815969056775, 0.0], 'a7': [1.1206147584281831, 0.0], 'a8': [-1.0, 0.0], 'a9': [7.411474127809773, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.615353236830009, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [17, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 17], 'central_character': '578.1', 'coefficient_field': 'CDF', 'conductor': 578, 'conductor_radical': 34, 'conjugate': '2184784845462951857781015507118', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [-3.2266815969056775, 0], [3.0, 0]], [[1.0, 0], [-1.1847925309040954, 0], [5.0, 0]], [[1.0, 0], [-1.1206147584281831, 0], [7.0, 0]], [[1.0, 0], [3.4114741278097727, 0], [11.0, 0]], [[1.0, 0], [-0.3472963553338607, 0], [13.0, 0]], 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'7.74161040975547886945699768277467', '8.018927480707213954673114043477082', '8.935862368630885126871719829127618', '9.731928029928731678294533603328056', '10.22930138279139119731815534076959'], 'prelabel': '2-578-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.14833731914474, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.72349135090505258963251456535', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.56050764196916455916413239937', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.64686034098190402595071896663', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 4.615353236830009, 'bad_primes': [2, 17], 'central_character': '1.1', 'conductor': 578, 'conductor_radical': 34, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/578/2/a/f/1/3'], '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': '2-578-1.1-c1-0-10', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-578-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.14833731914474, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.72349135090505258963251456535', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2184784845462951857781015507118', 'Lhash_array': ['2184784845462951857781015507118'], 'factors': ['2-578-1.1-c1-0-10'], 'label': '2-578-1.1-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/578/2/a/f/1/3'}