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lfunc_lfunctions • Show schema
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{'Lhash': '1392325974613052263050965809234', 'a10': [0, -0.3982106697545057], 'a2': [0, -0.3982106697545057], 'a3': [0, 0], 'a4': [1.841428262493668, 0], 'a5': [1.0, 0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, -1.5296977212214906], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.607013645692334, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 7], 'central_character': '2205.881', 'coefficient_field': 'CDF', 'conductor': 2205, 'conductor_radical': 105, 'conjugate': '1482800384452615312874783852791', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0.3982106697545057], [-2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -5.135237967635789], [-11.0, 0]], [[1.0, 0], [0, 5.095454484665174], [-13.0, 0]], [[1.0, 0], [-4.486242824183488, 0], [17.0, 0]], [[1.0, 0], [0, -3.801397829821418], 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'4.16582196429700684627358427839817', '5.52472574878728576185120811779358', '5.86694582743422186136978325873276', '6.77791974985075585579512835885493', '7.36399748007477047574151257757311', '8.329655693760264023020089451141429', '8.972433649236711568052292303223222'], 'prelabel': '2-2205-21.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.19607121551724, 'root_angle': 0.07690119815619134, 'root_number': '0.97095826429683353190130193259074594682080821794629164972 + 0.23924892683914041382986131482181962087045862213663535992*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.03845059907809567', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.09835152869597991041355818255', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.27211629477578584440012588267', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.13757670716876417625631698697', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.607013645692334, 'bad_primes': [3, 5, 7], 'central_character': '21.20', 'conductor': 2205, 'conductor_radical': 105, 'degree': 2, 'index': 33, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2205/2/b/b/881/6'], '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': '2-2205-21.20-c1-0-33', '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': '2-2205-21.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.19607121551724, 'root_angle': 0.03845059907809567, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.09835152869597991041355818255', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1392325974613052263050965809234', 'Lhash_array': ['1392325974613052263050965809234'], 'label': '2-2205-21.20-c1-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2205/2/b/b/881/6'}