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lfunc_lfunctions • Show schema
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{'Lhash': '2816628228252596782178947350372', 'a10': [-1.840626665989856, 1.3034791806126482e-60], 'a2': [-0.5271624205392119, -0.9130720962149061], 'a3': [0.0, 0.0], 'a4': [0.4441995647424781, -0.769376214833953], 'a5': [0.872893530663262, -1.5118959447069515], 'a6': [0.0, 0.0], 'a7': [-1.2296232956524367, -2.129770022240307], 'a8': [-3.045310953165284, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.244', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '731349206231830265820180181752', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5271624205392119, 0.9130720962149061], [-1.0, 1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.872893530663262, 1.5118959447069515], [-2.5, -4.330127018922194]], [[1.0, 0], [1.2296232956524367, 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'10.95450235084996937674413289008678'], 'prelabel': '2-3e6-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -1.0, 'root_number': '-1.0 - 1.2246467991473532e-16*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.5', 'prec': 14}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.22192789381039815608951698888', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.12456900298000725644776433212', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.43309039349044947179248004439', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '9.4', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/c/e/244/2'], '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': '2-3e6-9.4-c1-0-27', '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': '2-3e6-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.5, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.22192789381039815608951698888', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2816628228252596782178947350372', 'Lhash_array': ['2816628228252596782178947350372'], 'label': '2-3e6-9.4-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/c/e/244/2'}