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lfunc_lfunctions • Show schema
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{'Lhash': '1911255660510708927715769239586', 'a10': [4.164247938460211, 0.0], 'a2': [1.0, 0.0], 'a3': [-2.1642479384602114, 0.0], 'a4': [1.0, 0.0], 'a5': [4.164247938460211, 0.0], 'a6': [-2.1642479384602114, 0.0], 'a7': [-0.6839691391292742, 0.0], 'a8': [1.0, 0.0], 'a9': [1.6839691391292742, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.3377468044895218, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [11, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 11, 19], 'central_character': '418.1', 'coefficient_field': 'CDF', 'conductor': 418, 'conductor_radical': 418, 'conjugate': '1911255660510708927715769239586', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.1642479384602114, 0], [3.0, 0]], [[1.0, 0], [-4.164247938460211, 0], [5.0, 0]], [[1.0, 0], [0.6839691391292742, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-2.683969139129274, 0], [13.0, 0]], 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0], [107.0, 0]], [[1.0, 0], [-6.0, 0], [109.0, 0]], [[1.0, 0], [-10.432310711696067, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-418-1.1-c1-0-2', '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/418/2/a/h/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.872909514560645, 1.8721822304051734, 1.868000832143437, 1.8547129429472107, 1.823939449608972, 1.7658228693554607, 1.6703522741971406, 1.5286234987622203, 1.3339875614961048, 1.0830768183799675, 0.7766873771172981, 0.4204662681631569, 0.025324866402971616, -0.39251272946752247, -0.8119122280809841, -1.20774441810828, -1.5523339072577043, -1.8174070268202125, -1.9764405366947613, -2.0072463363182416, -1.8945668207471944, -1.6324099820145288, -1.2258319585306299, 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'6.86228195712903422927850873640133', '8.540511508341507227250707888884805', '9.828055502274430804721902238363181', '10.40866193169665718996320851585167', '11.15318713195075482282247711275494'], 'prelabel': '2-418-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8269501373845762, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.50771487045926067104229885805', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.01107070329188969587230374623', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.78676607391630482467669756030', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.3377468044895218, 'bad_primes': [2, 11, 19], 'central_character': '1.1', 'conductor': 418, 'conductor_radical': 418, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/418/2/a/h/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': '2-418-1.1-c1-0-2', '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': '2-418-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8269501373845762, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.50771487045926067104229885805', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1911255660510708927715769239586', 'Lhash_array': ['1911255660510708927715769239586'], 'label': '2-418-1.1-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/418/2/a/h/1/1'}