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  • lfunc_lfunctions • Show schema
    {'Lhash': '455707181240908726135510566512', 'a10': [52479.33290927325, 90896.8709461827], 'a2': [16.0, -27.712812921102035], 'a3': [121.5, 210.4441731196186], 'a4': [-512.0, -886.8100134752651], 'a5': [-1639.9791534147892, 2840.527217068209], 'a6': [7776.0, 0], 'a7': [-17084.739025348674, -41054.09157971624], 'a8': [-32768.0, 0], 'a9': [-29524.5, 51137.93406806732], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.27041358350274, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '5.5', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [-16.0, 27.712812921102035]]], [3, [[1.0, 0], [-121.5, -210.4441731196186]]], [7, [[1.0, 0], [17084.739025348674, 41054.09157971624]]]], 'bad_primes': [2, 3, 7], 'central_character': '42.37', 'coefficient_field': 'CDF', 'conductor': 42, 'conductor_radical': 42, 'conjugate': '1956346183898683449861353586948', 'degree': 2, 'euler_factors': [[[1.0, 0], [-16.0, 27.712812921102035]], [[1.0, 0], [-121.5, -210.4441731196186]], [[1.0, 0], 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'0.35948957950941894758679905946056', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.38722564863870628377707578942098', 'prec': 110}, 'z3': {'__RealLiteral__': 0, 'data': '4.01685612295515556389904437200398', 'prec': 110}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 32.27041358350274, 'bad_primes': [2, 3, 7], 'central_character': '7.2', 'conductor': 42, 'conductor_radical': 42, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/42/12/e/d/37/2'], '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': '2-42-7.2-c11-0-3', 'motivic_weight': 11, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [11], 'order_of_vanishing': 0, 'prelabel': '2-42-7.2-c11-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.680705377283946, 'root_angle': -0.23951628312568596, 'self_dual': False, 'spectral_label': 'c11-0', 'z1': {'__RealLiteral__': 0, 'data': '0.35948957950941894758679905946056', 'prec': 107}}
  • lfunc_instances • Show schema
    {'Lhash': '455707181240908726135510566512', 'Lhash_array': ['455707181240908726135510566512'], 'factors': ['2-42-7.2-c11-0-3'], 'label': '2-42-7.2-c11-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/42/12/e/d/37/2'}