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lfunc_lfunctions • Show schema
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{'Lhash': '469055457892221957544158509646', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.4313369051005815, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 62.28331357659873, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '7800.1', 'coefficient_field': 'CDF', 'conductor': 7800, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.4313369051005815, 0], [7.0, 0]], [[1.0, 0], [2.636746766506401, 0], [11.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [7.84215662791222, 0], [17.0, 0]], [[1.0, 0], [-0.7945901385941807, 0], [19.0, 0]], [[1.0, 0], [-3.4313369051005815, 0], [23.0, 0]], [[1.0, 0], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-7800-1.1-c1-0-3', 'leading_term': '0.56485774134694071481514581219601', '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/7800/2/a/bi/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [0.5648577413469407, 0.5556499674927636, 0.5280444844137339, 0.4821003541693744, 0.41793410970423844, 0.33574556068967265, 0.23585136634690762, 0.11872408333795022, -0.01496592798912343, -0.1643085014740995, -0.32811431206337727, -0.5048807640131314, -0.6927654579217208, -0.8895692491848389, -1.0927305414962896, -1.2993320650117297, -1.5061209817236336, -1.709542746925775, -1.905788738375386, -2.0908572454599788, -2.260626991153485, -2.4109419430216925, -2.537705761292309, -2.6369838395959695, -2.7051105271016547, 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'4.90291986094831428099672982859211', '6.06637924896741067587609129200209', '6.33926956923891183443138056978667', '6.99377539923101745189646758395039', '7.75625601805080866672477189896654'], 'prelabel': '2-7800-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.8919777987902835, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.37001951311171439947614146040', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.75692941219339960756662673265', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.82491329707701183641655208417', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 62.28331357659873, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 7800, 'conductor_radical': 390, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7800/2/a/bi/1/1'], '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': '2-7800-1.1-c1-0-3', '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': '2-7800-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.8919777987902835, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.37001951311171439947614146040', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '469055457892221957544158509646', 'Lhash_array': ['469055457892221957544158509646'], 'label': '2-7800-1.1-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7800/2/a/bi/1/1'}