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lfunc_lfunctions • Show schema
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{'Lhash': '1747273602827103321403400395630', 'a10': [0.0, 0.0], 'a2': [0.8168617105478098, 1.4148459854264284], 'a3': [0.0, 0.0], 'a4': [-0.3345261083181875, 0.5794162160653904], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.2526741746500389, -0.4376445082543994], 'a8': [2.1744005659364527, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.389902136436429, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '675.226', 'coefficient_field': 'CDF', 'conductor': 675, 'conductor_radical': 15, 'conjugate': '1843130144813241341752536002490', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8168617105478098, -1.4148459854264284], [-1.0, 1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.2526741746500389, 0.4376445082543994], [-3.5, 6.06217782649107]], [[1.0, 0], [-1.5501014630819558, -2.6848544909447996], 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'0.4680684270736324 - 0.8836922244632549*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.17247503656', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.37835583599496737815986596781', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.59822715710740763693091224356', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.79120314296459164973731016058', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.389902136436429, 'bad_primes': [3, 5], 'central_character': '9.4', 'conductor': 675, 'conductor_radical': 15, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/675/2/e/c/226/4'], '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': '2-675-9.4-c1-0-9', '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': '2-675-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.321616276742655, 'root_angle': -0.17247503655968693, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.37835583599496737815986596781', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1747273602827103321403400395630', 'Lhash_array': ['1747273602827103321403400395630'], 'label': '2-675-9.4-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/675/2/e/c/226/4'}