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lfunc_lfunctions • Show schema
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{'Lhash': '938783655821328807968450001889', 'a10': [-0.1501683474320005, -0.26009920744088016], 'a2': [1.0268225729490117, 1.778508866706288], 'a3': [0, 0], 'a4': [-1.1087291926352567, 1.9203752934790856], 'a5': [-0.14624566248161094, 0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [-0.4465823573456119, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.5642081874154, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '1323.667', 'coefficient_field': 'CDF', 'conductor': 1323, 'conductor_radical': 21, 'conjugate': '2128093953678377499555121403866', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0268225729490117, -1.778508866706288], [-1.0, 1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.14624566248161094, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.6640407426161252, 0], [11.0, 0]], [[1.0, 0], [0.09994540418981711, 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'6.90770086190929098580227621256736', '7.53143072058734623861675774654931', '8.744406650918856873207685790538393', '9.512913621031152551260563369491558'], 'prelabel': '2-1323-63.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.250262787439717, 'root_angle': -0.8517431328513042, 'root_number': '-0.89347930047709773186354220327178645124856583117022434218 - 0.4491043749719613951406516851330361447592728064325312425*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4258715664256521', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.74056972453790423242065736501', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.23788298637031179939629658456', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.96003217703926217581328118601', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.5642081874154, 'bad_primes': [3, 7], 'central_character': '63.16', 'conductor': 1323, 'conductor_radical': 21, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1323/2/g/f/667/5'], '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': '2-1323-63.16-c1-0-11', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1323-63.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.250262787439717, 'root_angle': -0.4258715664256521, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.74056972453790423242065736501', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '938783655821328807968450001889', 'Lhash_array': ['938783655821328807968450001889'], 'label': '2-1323-63.16-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1323/2/g/f/667/5'}