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lfunc_lfunctions • Show schema
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{'Lhash': '2667643460856862447054634616635', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [2.6016791318831545, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 1.0], 'a6': [0.0, 0.0], 'a7': [0.0, -2.768734305276283], 'a8': [0.0, 0.0], 'a9': [3.768734305276283, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.076110452553291, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, -1.0]]], [13, [[1.0, 0], [0.1670551733931289, -3.6016791318831545]]]], 'bad_primes': [2, 5, 13], 'central_character': '260.181', 'coefficient_field': 'CDF', 'conductor': 260, 'conductor_radical': 130, 'conjugate': '2487562765340713106115890064125', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.6016791318831545, 0], [3.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 2.768734305276283], [-7.0, 0]], [[1.0, 0], [0, 2.1670551733931287], [-11.0, 0]], [[1.0, 0], [0.1670551733931289, -3.6016791318831545]], [[1.0, 0], 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'5.86319560045262701450559114725200', '7.46351719007087030448137519389763', '8.205474628081237563833072737878471', '9.138356089791773384266449276254247', '9.613574490610498590131044292873656', '10.99662253907658446783162451049412', '12.39685749323058580939921505369981'], 'prelabel': '2-260-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': 0.01475346016023625, 'root_number': '0.9989260605979493 + 0.04633276873080413*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.00737673008012', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.10439963533845728292280067901', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.12866801358526577020037976333', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.57530830853088334042073220885', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.076110452553291, 'bad_primes': [2, 5, 13], 'central_character': '13.12', 'conductor': 260, 'conductor_radical': 130, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/260/2/f/a/181/6'], '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': '2-260-13.12-c1-0-4', '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': '2-260-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': 0.007376730080118125, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.10439963533845728292280067901', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2667643460856862447054634616635', 'Lhash_array': ['2667643460856862447054634616635'], 'label': '2-260-13.12-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/260/2/f/a/181/6'}