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  • lfunc_lfunctions • Show schema
    {'Lhash': '854078701338656852467609627945', 'a10': [-0.0980171403295606, 0.9951847266721969], 'a2': [-0.881921264348355, -0.47139673682599764], 'a3': [-1.7681951800349338, -0.7324104244932061], 'a4': [0.5555702330196022, 0.8314696123025452], 'a5': [-0.3826834323650898, -0.9238795325112867], 'a6': [1.214153044667635, 1.479449765530889], 'a7': [0.0, 0.0], 'a8': [-0.0980171403295606, -0.9951847266721969], 'a9': [1.8829823836059063, 1.8829823836059063], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5171576384043273, 'analytic_normalization': 0, 'bad_lfactors': [[2, [[1.0, 0], [0.881921264348355, 0.47139673682599764]]], [5, [[1.0, 0], [0.3826834323650898, 0.9238795325112867]]], [19, [[1.0, 0], [-0.3826834323650898, 0.9238795325112867]]]], 'bad_primes': [2, 5, 19], 'central_character': '3040.189', 'coefficient_field': 'CDF', 'conductor': 3040, 'conductor_radical': 190, 'conjugate': '540933392981902476284462586859', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'rational': False, 'root_analytic_conductor': 1.2317295313518821, 'root_angle': 0.296875, 'root_number': '-0.29028467725446236763619237581754 + 0.95694033573220886493579788698009*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.296875', 'prec': 20}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.67374929746799903186861107987', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '2.57829329223365177149594870343', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.63358228575017389180424002250', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 1.5171576384043273, 'bad_primes': [2, 5, 19], 'central_character': '3040.189', 'conductor': 3040, 'conductor_radical': 190, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3040/1/cn/a/189/2'], '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': '2-3040-3040.189-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3040-3040.189-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2317295313518821, 'root_angle': 0.296875, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.67374929746799903186861107987', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '854078701338656852467609627945', 'Lhash_array': ['854078701338656852467609627945'], 'factors': ['2-3040-3040.189-c0-0-1'], 'label': '2-3040-3040.189-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3040/1/cn/a/189/2'}