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  • lfunc_lfunctions • Show schema
    {'Lhash': '1113304288535278379355596013258', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, -1.4142135623730951], 'a6': [0, 0], 'a7': [-3.1622776601683795, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.795065251406015, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '4608.2305', 'coefficient_field': 'CDF', 'conductor': 4608, 'conductor_radical': 6, 'conjugate': '355656526724481259938263464058', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.4142135623730951], [-5.0, 0]], [[1.0, 0], [3.1622776601683795, 0], [7.0, 0]], [[1.0, 0], [0, -4.47213595499958], [-11.0, 0]], [[1.0, 0], [0, -4.47213595499958], [-13.0, 0]], [[1.0, 0], [6.324555320336759, 0], [17.0, 0]], [[1.0, 0], [0, 2.8284271247461903], [-19.0, 0]], [[1.0, 0], [-4.0, 0], [23.0, 0]], 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'7.72541383604421495702031541456041', '8.666438264618881848490867712512217'], 'prelabel': '2-4608-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.065893606996912, 'root_angle': 0.25, 'root_number': '0.e-55 + 1.0000000000000000000000000000000000000000000000000000000*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 7}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.878242228840374217547190646074', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.47680254987283298954188427455', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.20975549532666909201892769790', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 36.795065251406015, 'bad_primes': [2, 3], 'central_character': '8.5', 'conductor': 4608, 'conductor_radical': 6, 'degree': 2, 'index': 45, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4608/2/d/l/2305/1'], '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': '2-4608-8.5-c1-0-45', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-4608-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.065893606996912, 'root_angle': 0.25, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.878242228840374217547190646074', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1113304288535278379355596013258', 'Lhash_array': ['1113304288535278379355596013258'], 'factors': ['2-4608-8.5-c1-0-45'], 'label': '2-4608-8.5-c1-0-45', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4608/2/d/l/2305/1'}