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lfunc_lfunctions • Show schema
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{'Lhash': '2500229417741126473463501172192', 'a10': [-1.8157443364618535, 0.6420781528225403], 'a2': [-0.7304241599611887, 0.456419671453863], 'a3': [-0.019324650970859485, -0.005541254497293426], 'a4': [-0.5515417566131988, 1.130828182375435], 'a5': [2.1828483087809643, 0.484946657738853], 'a6': [0.016644329509030116, -0.004772684685763551], 'a7': [-1.4382950582526604, -2.491200117168846], 'a8': [-0.29333361655668894, -2.7908829345955186], 'a9': [-2.543801551835536, -1.5895436270814132], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.79289409601082, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-2.1828483087809643, -0.484946657738853]]], [19, [[1.0, 0], [-0.5948504385389289, 4.318119145620005]]]], 'bad_primes': [5, 19], 'central_character': '475.396', 'coefficient_field': 'CDF', 'conductor': 475, 'conductor_radical': 95, 'conjugate': '397655709537999315433451200227', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[66.99579959635766, 41.86362187442319]], [[1.0, 0], [-14.948373138473926, -6.655444519944182], [55.53784032778523, 61.68102051462372]], [[1.0, 0], [-4.875789706396688, 6.240726235035589], [-21.531048708370427, -86.35631963856369]], [[1.0, 0], [-2.0786939961309288, -8.337186246337362], [-85.64591650731592, 45.5387415902314]], [[1.0, 0], [13.465981456069873, 4.901216425190088], [77.37048875501678, 64.92154857834048]], [[1.0, 0], [8.09252731786117, -3.603025298554743], [68.9204524549624, -76.5439170241716]], [[1.0, 0], [5.916765737650823, 10.248138874093971], [-53.5, 92.66471820493493]], [[1.0, 0], [18.250831036431546, -2.564987027872401], [104.77752485727676, -30.044471784052913]], [[1.0, 0], [4.918801362916017, 15.138513977281825], [-91.41892036436906, 66.41973350904946]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 35, 'label': '2-475-475.396-c1-0-35', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': 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1.9475353901818626, 'root_angle': 0.5534799722014154, 'root_number': '-0.16722295725451716 + 0.9859191054884036*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.276739986101', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.97233324173946830313435727484', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.72384673526658627036271848148', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.06733667268205359103836286795', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.79289409601082, 'bad_primes': [5, 19], 'central_character': '475.396', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'index': 35, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/2/bc/a/396/19'], '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': '2-475-475.396-c1-0-35', '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': '2-475-475.396-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.2767399861007077, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.97233324173946830313435727484', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2500229417741126473463501172192', 'Lhash_array': ['2500229417741126473463501172192'], 'label': '2-475-475.396-c1-0-35', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/bc/a/396/19'}