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lfunc_lfunctions • Show schema
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{'Lhash': '1248513326399260083993728863952', 'a10': [-2.175327747161075, 0.0], 'a2': [2.175327747161075, 0.0], 'a3': [-1.0, 0.0], 'a4': [2.732050807568877, 0.0], 'a5': [-1.0, 0.0], 'a6': [-2.175327747161075, 0.0], 'a7': [-0.4432769395921976, 0.0], 'a8': [1.5924504340362513, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20.242076912394587, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 13], 'central_character': '2535.1', 'coefficient_field': 'CDF', 'conductor': 2535, 'conductor_radical': 195, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.175327747161075, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0.4432769395921976, 0], [7.0, 0]], [[1.0, 0], [-1.5924504340362513, 0], [11.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.7677781811973263, 0], [17.0, 0]], [[1.0, 0], 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'3.41376348200194829867870578847964', '4.28648467496177210343755690342222', '4.80111232549878963614820562757389', '5.84277852529084063988665165202241', '6.18586784260321296075423182301991', '7.14264917217740755200061555961025', '7.80445072421324979278110006791732', '8.936121723089860217318773170956389'], 'prelabel': '2-2535-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.499119570804336, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.984903352843816885537772188385', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.57868157691315766289305029873', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.41376348200194829867870578848', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 20.242076912394587, 'bad_primes': [3, 5, 13], 'central_character': '1.1', 'conductor': 2535, 'conductor_radical': 195, 'degree': 2, 'index': 41, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2535/2/a/bj/1/4'], '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': '2-2535-1.1-c1-0-41', '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': '2-2535-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.499119570804336, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.984903352843816885537772188385', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1248513326399260083993728863952', 'Lhash_array': ['1248513326399260083993728863952'], 'factors': ['2-2535-1.1-c1-0-41'], 'label': '2-2535-1.1-c1-0-41', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2535/2/a/bj/1/4'}