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lfunc_lfunctions • Show schema
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{'Lhash': '640620605820819437683046465045', 'a10': [-1.0, -1.7320508075688772], 'a2': [-0.5, 0.8660254037844386], 'a3': [-0.5, -0.8660254037844386], 'a4': [-0.5, -0.8660254037844386], 'a5': [-1.0, 1.7320508075688772], 'a6': [1.0, -3.111507638930571e-61], 'a7': [0.0, 0.0], 'a8': [1.0, 0.0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.3476018194256443, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, -0.8660254037844386]]], [3, [[1.0, 0], [0.5, 0.8660254037844386]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '294.79', 'coefficient_field': 'CDF', 'conductor': 294, 'conductor_radical': 42, 'conjugate': '2586932439276244677575184272500', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [1.0, -1.7320508075688772], [-2.5, -4.330127018922194]], [[1.0, 0], [0, 0]], [[1.0, 0], 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-2.68522538144804, -1.9481429374110777, -1.0313553132067843, -0.26818835868375446, 0.08883991578167702], 'positive_zeros': ['0.50536055101104460612865375099906', '2.71582742669109014304947578532152', '4.21536856473896139180963478796373', '4.97636167220636002120561114834697', '6.47275686945982252098654723090157', '7.88157836693051664150520105717870', '8.766647804035256629565796305818130', '9.571322768419506760571051977178222', '10.48893098039013274090130252498378', '11.52139013956716966692339485736626'], 'prelabel': '2-294-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5321885717579427, 'root_angle': -0.7473584788824512, 'root_number': '-0.7012145161459064 - 0.7129503505478221*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.373679239441', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.50536055101104460612865375100', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.71582742669109014304947578532', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.21536856473896139180963478796', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.3476018194256443, 'bad_primes': [2, 3, 7], 'central_character': '7.2', 'conductor': 294, 'conductor_radical': 42, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/294/2/e/a/79/1'], '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': '2-294-7.2-c1-0-0', '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': '2-294-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5321885717579427, 'root_angle': -0.3736792394412256, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.50536055101104460612865375100', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '640620605820819437683046465045', 'Lhash_array': ['640620605820819437683046465045'], 'label': '2-294-7.2-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/294/2/e/a/79/1'}