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lfunc_lfunctions • Show schema
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{'Lhash': '2293215184392111407058042257360', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.082392200292394, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.082392200292394, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-1.82842712474619, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.309192042213452, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 7], 'central_character': '1792.1', 'coefficient_field': 'CDF', 'conductor': 1792, 'conductor_radical': 14, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.082392200292394, 0], [3.0, 0]], [[1.0, 0], [1.082392200292394, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-5.226251859505506, 0], [11.0, 0]], [[1.0, 0], [6.3086440597979, 0], [13.0, 0]], [[1.0, 0], [-3.65685424949238, 0], [17.0, 0]], [[1.0, 0], [4.1438596592131125, 0], [19.0, 0]], [[1.0, 0], [1.17157287525381, 0], [23.0, 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'GL2', 'index': 39, 'label': '2-1792-1.1-c1-0-39', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1792/2/a/u/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.5405609110720697e-60, 0.16058170109876954, 0.321166335060264, 0.4817153874740798, 0.6421095607770816, 0.8021134896941404, 0.961346133862823, 1.1192580668523935, 1.2751164400636323, 1.4279979790559914, 1.576790008066827, 1.7201992163786557, 1.8567676803442497, 1.9848955265193273, 2.102869546305226, 2.2088970307274285, 2.3011440675844486, 2.3777775187084624, 2.43700986410925, 2.477146058730696, 2.4966314967291345, 2.4941001207023668, 2.468421654083681, 2.418746879855867, 2.344549844036217, 2.245665834070903, 2.1223239758917716, 1.9751733137307916, 1.805301287752921, 1.6142436090242207, 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'8.771658653318540243429935297066199'], 'prelabel': '2-1792-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7827492703341377, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.80902780622613050753272117026', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.94079090463619968806675059787', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.71720930541563799753300226314', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.309192042213452, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 1792, 'conductor_radical': 14, 'degree': 2, 'index': 39, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1792/2/a/u/1/3'], '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': '2-1792-1.1-c1-0-39', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-1792-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7827492703341377, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.80902780622613050753272117026', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2293215184392111407058042257360', 'Lhash_array': ['2293215184392111407058042257360'], 'label': '2-1792-1.1-c1-0-39', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1792/2/a/u/1/3'}