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lfunc_lfunctions • Show schema
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{'Lhash': '4554665697471656003212624789262', 'a10': [-1.7915787619285775, 1.7856845128927619], 'a2': [0.3682757009993502, -1.3654204510162564], 'a3': [-0.3905483736686061, -1.6874453969906127], 'a4': [-1.7287460161068744, -1.0057023475137215], 'a5': [-1.549002538705787, -0.8943170326971999], 'a6': [-2.4479019311111907, -0.08818239995659108], 'a7': [2.635730879701317, 0.2300494072779199], 'a8': [-2.0098617038618865, 1.9900894279778973], 'a9': [-2.6949439356496137, 1.3180581108985183], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.3682757009993502, 1.3654204510162564]]], [3, [[1.0, 0], [0.3905483736686061, 1.6874453969906127]]], [7, [[1.0, 0], [-2.635730879701317, -0.2300494072779199]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.5', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': 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'5.62707729053860891988601596776678', '6.91759098290872004039071015442193', '8.202427590713049593523126202036437', '8.831155582053932557081189339893515', '10.35468236987309787457546864024988', '11.16516559393985439739512081996848', '12.22197372357444516136270884781908', '13.51795270321520604089076738892701'], 'prelabel': '2-168-168.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.9139021270507026, 'root_number': '-0.9636415665285333 + 0.26719829950513224*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.456951063525', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.59299770508658165538807470125', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.51023570115278900626199459260', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.62707729053860891988601596777', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.341486753957511, 'bad_primes': [2, 3, 7], 'central_character': '168.5', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/ba/c/5/15'], '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': '2-168-168.5-c1-0-27', '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': '2-168-168.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.4569510635253513, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.59299770508658165538807470125', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4554665697471656003212624789262', 'Lhash_array': ['4554665697471656003212624789262'], 'label': '2-168-168.5-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/ba/c/5/15'}