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lfunc_lfunctions • Show schema
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{'Lhash': '3519393882385189017707847142902', 'a10': [0.0, -2.584225443216521], 'a2': [-0.7071067811865476, -0.7071067811865476], 'a3': [1.2921127216082604, -1.1534490516091702], 'a4': [0.0, 1.0], 'a5': [1.8273233350132132, 1.8273233350132132], 'a6': [-1.7292733136526428, -0.09805002136057041], 'a7': [-2.6312232922920726, -2.6312232922920726], 'a8': [0.7071067811865476, -0.7071067811865476], 'a9': [0.339110570683812, -2.9807723866223834], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6228331357659873, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]], [3, [[1.0, 0], [-1.2921127216082604, 1.1534490516091702]]], [13, [[1.0, 0], [-1.6312232922920724, -3.2154487355085934]]]], 'bad_primes': [2, 3, 13], 'central_character': '78.5', 'coefficient_field': 'CDF', 'conductor': 78, 'conductor_radical': 78, 'conjugate': '2741858796657855411558889476558', 'degree': 2, 'euler_factors': 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3.384438435221587, 4.6279421778672445, 5.496966959556527, 5.773304962209691, 5.3248347555823, 4.135815237352584, 2.3160054687396183, 0.08613407016486022, -2.258055445272658, -4.3965998374876625, -6.041270190590091, -6.985834358481275, -7.140815873009308, -6.546001735493271, -5.358428943571723, -3.8185484693541176, -2.2016865222066517, -0.764860432937274, 0.30016918478590676, 0.898200005744023, 1.0402911143824163, 0.8306177758136194, 0.43415762179567785], 'positive_zeros': ['2.77631224388767136300601664668059', '5.09243984126932801547268944305412', '6.16084661545106261305615036813399', '8.193887357286899242019551428131095', '8.991474965099147750011110009253072', '9.722223408874537875180553737954421', '10.90296466376379646690816320258587', '13.01713840793942274569321515193075', '13.35490521620321988185556713510806', '14.96541428774710529013131258704695'], 'prelabel': '2-78-39.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7891977798790284, 'root_angle': 0.2750062141857105, 'root_number': '0.6494332032264509 + 0.760418644265796*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.137503107093', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.77631224388767136300601664668', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.09243984126932801547268944305', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.16084661545106261305615036813', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6228331357659873, 'bad_primes': [2, 3, 13], 'central_character': '39.5', 'conductor': 78, 'conductor_radical': 78, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/78/2/g/a/5/3'], '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': '2-78-39.5-c1-0-3', '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': '2-78-39.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7891977798790284, 'root_angle': 0.13750310709285524, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.77631224388767136300601664668', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3519393882385189017707847142902', 'Lhash_array': ['3519393882385189017707847142902'], 'label': '2-78-39.5-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/78/2/g/a/5/3'}