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  • lfunc_lfunctions • Show schema
    {'Lhash': '290792366620390071527217856035', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-5.18992146556276, 14.699139946993188], 'a4': [0, 0], 'a5': [-64.31626263290066, 0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [-189.1294303625818, -152.57476387242198], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 94.30568605003263, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [5.18992146556276, -14.699139946993188]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '588.293', 'coefficient_field': 'CDF', 'conductor': 588, 'conductor_radical': 42, 'conjugate': '1135223350487735276583627123713', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [5.18992146556276, -14.699139946993188]], [[1.0, 0], [64.31626263290066, 0], [3125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 593.7504006513597], [-161051.0, 0]], [[1.0, 0], [0, -1199.213760115256], [-371293.0, 0]], [[1.0, 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1.5790643507686835, 1.8068944545360104, 1.9084781471555732, 1.8855273966806183, 1.7466465225212686], 'positive_zeros': ['0.22939472956352124922469749346004', '1.25138137872761374672836576282453', '2.66392143716459905831892226340224', '3.75161768839474217656224802170629', '5.05784534119355931979492728316488', '5.86068476977959723914319515552414', '7.16580886746909812128523250124378', '7.78351388869942921794635353103733', '8.114265246527046968402511748720480', '9.686276444719529796139717478616067'], 'prelabel': '2-588-21.20-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.711111473463408, 'root_angle': -0.4209608385386742, 'root_number': '-0.8791991010106305931064826578202978176045197351123978607 - 0.4764545526932227595914504937075567223724576576633358445*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4209608385386743', 'prec': 54}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.22939472956352124922469749346', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '1.25138137872761374672836576282', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.66392143716459905831892226340', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 94.30568605003263, 'bad_primes': [2, 3, 7], 'central_character': '21.20', 'conductor': 588, 'conductor_radical': 42, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/588/6/f/c/293/18'], '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': '2-588-21.20-c5-0-6', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-588-21.20-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.711111473463408, 'root_angle': -0.4209608385386742, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.22939472956352124922469749346', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '290792366620390071527217856035', 'Lhash_array': ['290792366620390071527217856035'], 'factors': ['2-588-21.20-c5-0-6'], 'label': '2-588-21.20-c5-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/588/6/f/c/293/18'}