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lfunc_lfunctions • Show schema
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{'Lhash': '1056681061374701080750243845347', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-0.6213203435596426, 0.3587194676071504], 'a4': [0, 0], 'a5': [5.742640687119285, 3.3155151465676167], 'a6': [0, 0], 'a7': [6.242640687119285, 3.166928677997479], 'a8': [0, 0], 'a9': [-4.242640687119285, 7.3484692283495345], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.207115843341303, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-6.242640687119285, -3.166928677997479]]]], 'bad_primes': [2, 7], 'central_character': '448.257', 'coefficient_field': 'CDF', 'conductor': 448, 'conductor_radical': 14, 'conjugate': '2330586770794388700312965298003', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.6213203435596426, -0.3587194676071504], [4.5, -7.794228634059948]], [[1.0, 0], [-5.742640687119285, -3.3155151465676167], [12.5, 21.650635094610966]], [[1.0, 0], [-6.242640687119285, 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'6.94314861908577661543133487487991', '7.968640808144406819314521606870383', '8.979791701551711869520533024122892', '9.705564343798989456677264102593617', '10.68322231136547491066503361923290'], 'prelabel': '2-448-7.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.49386832083599, 'root_angle': -0.4768821436017044, 'root_number': '0.0725630575822229325785675228760462742240334855891341603 - 0.99736382663214681027272156287330090368331122723502673198*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2384410718008522', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.833574378605946227783919683364', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.11557842776077351742022583051', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.75392381254251300740933194488', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.207115843341303, 'bad_primes': [2, 7], 'central_character': '7.5', 'conductor': 448, 'conductor_radical': 14, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/448/3/s/d/257/1'], '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': '2-448-7.5-c2-0-13', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-448-7.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.49386832083599, 'root_angle': -0.2384410718008522, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.833574378605946227783919683364', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1056681061374701080750243845347', 'Lhash_array': ['1056681061374701080750243845347'], 'label': '2-448-7.5-c2-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/448/3/s/d/257/1'}