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lfunc_lfunctions • Show schema
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{'Lhash': '2350438766228503649914701290201', 'a10': [2.2071067811865475, 3.822821082744905], 'a2': [-0.5, 0.8660254037844386], 'a3': [0.5, 0.8660254037844386], 'a4': [-0.5, -0.8660254037844386], 'a5': [2.2071067811865475, -3.822821082744905], 'a6': [-1.0, 0.0], 'a7': [1.6213203435596426, -2.0907702751760278], 'a8': [1.0, 0.0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.372062081298178, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, -0.8660254037844386]]], [3, [[1.0, 0], [-0.5, -0.8660254037844386]]], [7, [[1.0, 0], [-1.6213203435596426, 2.0907702751760278]]], [19, [[1.0, 0], [0.5, -0.8660254037844386]]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '798.457', 'coefficient_field': 'CDF', 'conductor': 798, 'conductor_radical': 798, 'conjugate': '1133620172604144563206751370259', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], 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[0]], 'group': 'GL2', 'index': 17, 'label': '2-798-7.2-c1-0-17', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/798/2/j/h/457/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.602841022618228, 1.721120818028693, 1.8251045519844251, 1.9114798228959171, 1.9733767151800505, 2.00168072670237, 1.9867468590637456, 1.9202136726803465, 1.7967109317907892, 1.6153145882778013, 1.380616575631673, 1.103270085482091, 0.7998726306705845, 0.49207750438912595, 0.20488604486847542, -0.03583365843578383, -0.206440297525911, -0.28894025428759346, -0.2743385300941068, -0.16544218995231752, 0.021388102132219613, 0.25599950762178786, 0.4960592950354612, 0.6906543820475752, 0.7857493951581116, 0.7310741958362257, 0.4877169093023623, 0.03545733472478212, -0.6212622308332225, 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'8.679813850381861875854376969483033', '9.721780270303666700972248371826961', '10.29121849949318155703928642187100'], 'prelabel': '2-798-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.524294372948246, 'root_angle': 0.18978452306496227, 'root_number': '0.8274608818879864 + 0.5615233645585515*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0948922615325', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.85416925279357554130139184771', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.48752745332071949595791546200', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.38285843419802107568911980762', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.372062081298178, 'bad_primes': [2, 3, 7, 19], 'central_character': '7.2', 'conductor': 798, 'conductor_radical': 798, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/798/2/j/h/457/2'], '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': '2-798-7.2-c1-0-17', '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': '2-798-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.524294372948246, 'root_angle': 0.09489226153248113, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.85416925279357554130139184771', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2350438766228503649914701290201', 'Lhash_array': ['2350438766228503649914701290201'], 'label': '2-798-7.2-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/798/2/j/h/457/2'}