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lfunc_lfunctions • Show schema
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{'Lhash': '154895046827239618696920006269', 'a10': [0.0, 0.0], 'a2': [0.25881904510252074, 0.9659258262890683], 'a3': [0.0, 0.0], 'a4': [-0.8660254037844386, 0.5], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [-0.7071067811865476, -0.7071067811865476], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6827209372819473, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.25881904510252074, -0.9659258262890683]]], [3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 3, 19], 'central_character': '1368.125', 'coefficient_field': 'CDF', 'conductor': 1368, 'conductor_radical': 114, 'conjugate': '3258647362896731481765613808994', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.25881904510252074, -0.9659258262890683]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [1.4142135623730951, 0], [1.0, 0]], [[1.0, 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'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.12219064685438725820572970355', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.24081155348599780146611428612', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.83745098967168823708320291643', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6827209372819473, 'bad_primes': [2, 3, 19], 'central_character': '456.125', 'conductor': 1368, 'conductor_radical': 114, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1368/1/bw/a/125/3'], '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': '2-1368-456.125-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1368-456.125-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.82626928859903, 'root_angle': 0.35574666064318006, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.12219064685438725820572970355', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '154895046827239618696920006269', 'Lhash_array': ['154895046827239618696920006269'], 'label': '2-1368-456.125-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1368/1/bw/a/125/3'}