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lfunc_lfunctions • Show schema
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{'Lhash': '2765661037540947498099434257007', 'a10': [0.0, 0.0], 'a2': [2.772092547743646, 4.801405135975049], 'a3': [-0.32081921699137633, -5.186239006255789], 'a4': [-11.36899418651172, 19.691675561993495], 'a5': [0.0, 0.0], 'a6': [24.011894040435937, -15.917117536240976], 'a7': [-12.856329690662566, -22.267816223083834], 'a8': [-81.71013547518157, 0.0], 'a9': [-26.79415006001808, 3.3276902742342322], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.275429751291645, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.32081921699137633, 5.186239006255789]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '225.76', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '184888252763776003642209691715', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.772092547743646, -4.801405135975049], [-4.0, 6.928203230275509]], [[1.0, 0], [0.32081921699137633, 5.186239006255789]], 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[-721448.5, -1249585.457044355]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 44, 'label': '2-15e2-9.4-c3-0-44', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/225/4/e/f/76/12', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.5138667853152562, 0.9064861751064603, 1.2515128152238, 1.545812278027582, 1.786297920403377, 1.9699732239820804, 2.0941203909996435, 2.156615483572435, 2.1563359299185527, 2.093614815369812, 1.970688484859763, 1.7920798744893998, 1.5648599499476863, 1.298734046433481, 1.0059091997501364, 0.700713013504181, 0.39895414808475577, 0.11703851028953485, -0.1291176629763986, -0.32530847396934703, -0.46029698705339084, -0.5269945306705652, -0.5234303591354247, -0.45338000671105266, -0.32653362064927294, -0.1581142777960751, 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'8.964733298859284800412875808978433', '9.285532969341282381904984967553859', '10.32840771308735584337059624223425', '11.15934380336843707482988560450212', '11.88408412234072527470596459262089'], 'prelabel': '2-15e2-9.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': 0.40511345008933836, 'root_number': '0.2936996485831705 + 0.9558977541673179*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.202556725045', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.18172186960903455697200470698', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.22927883503625286679734765036', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.25746465217846788836206118531', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.275429751291645, 'bad_primes': [3, 5], 'central_character': '9.4', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 44, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/4/e/f/76/12'], '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': '2-15e2-9.4-c3-0-44', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-15e2-9.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': 0.20255672504466918, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.18172186960903455697200470698', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2765661037540947498099434257007', 'Lhash_array': ['2765661037540947498099434257007'], 'label': '2-15e2-9.4-c3-0-44', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/4/e/f/76/12'}