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lfunc_lfunctions • Show schema
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{'Lhash': '2444800826329167174723911057051', 'a10': [0.5, 0.8660254037844386], 'a2': [-0.7071067811865476, 0.7071067811865476], 'a3': [-0.8660254037844386, 0.5], 'a4': [0.0, -1.0], 'a5': [0.25881904510252074, -0.9659258262890683], 'a6': [0.25881904510252074, -0.9659258262890683], 'a7': [-1.224744871391589, -1.224744871391589], 'a8': [0.7071067811865476, 0.7071067811865476], 'a9': [0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7785414197074838, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [3, [[1.0, 0], [0.8660254037844386, -0.5]]], [5, [[1.0, 0], [-0.25881904510252074, 0.9659258262890683]]], [13, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1560.467', 'coefficient_field': 'CDF', 'conductor': 1560, 'conductor_radical': 390, 'conjugate': '265425770181321478272962485804', 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6.1300972163766705], 'positive_zeros': ['1.92860779294310448984809269966392', '2.66401420579489821608268820433955', '3.67525505282066173698859503500816', '5.07609862328701178739803568744167', '6.21378039416327216439320269639451', '6.72021301413702601418885603234747', '7.30656540929053864664443144615162', '8.609875779345686692446247726665481', '9.277940023054684223910115172105234', '9.915098115038396683773666851808253'], 'prelabel': '2-1560-1560.467-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8823499417507114, 'root_angle': 0.7404584754918834, 'root_number': '-0.68559636052154760152608890926612 + 0.72798188881290729909006734791914*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.37022923774594163', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.92860779294310448984809269966', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.66401420579489821608268820434', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.67525505282066173698859503501', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7785414197074838, 'bad_primes': [2, 3, 5, 13], 'central_character': '1560.467', 'conductor': 1560, 'conductor_radical': 390, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1560/1/cs/f/467/1'], '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': '2-1560-1560.467-c0-0-14', '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': '2-1560-1560.467-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8823499417507114, 'root_angle': 0.3702292377459417, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.92860779294310448984809269966', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2444800826329167174723911057051', 'Lhash_array': ['2444800826329167174723911057051'], 'label': '2-1560-1560.467-c0-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1560/1/cs/f/467/1'}