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lfunc_lfunctions • Show schema
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{'Lhash': '1807213874962817602440880814390', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0.3472963553338607, 0.6015349327217412], 'a6': [0, 0], 'a7': [0.3054072893322786, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.923534996511162, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-3.064177772475912, 3.1001313808715523]]]], 'bad_primes': [2, 3, 19], 'central_character': '1368.577', 'coefficient_field': 'CDF', 'conductor': 1368, 'conductor_radical': 114, 'conjugate': '592083357689682644469393507557', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.3472963553338607, -0.6015349327217412], [-2.5, 4.330127018922194]], [[1.0, 0], [-0.3054072893322786, 0], [7.0, 0]], [[1.0, 0], [4.822948255619545, 0], [11.0, 0]], [[1.0, 0], [0.5, -0.8660254037844386], [-6.5, 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'root_analytic_conductor': 3.305077154396121, 'root_angle': 0.48256341915612855, 'root_number': '0.0547512426960612125779543337808964031437010446933099891 + 0.9985000257502435356269998002287647820247817129963582550*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.24128170957806427', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.42564037333114073648210165034', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.65091461773479678851816683072', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.71096428534882567228945134019', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.923534996511162, 'bad_primes': [2, 3, 19], 'central_character': '19.7', 'conductor': 1368, 'conductor_radical': 114, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1368/2/s/j/577/2'], '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': '2-1368-19.7-c1-0-18', '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': '2-1368-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.305077154396121, 'root_angle': 0.24128170957806427, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.42564037333114073648210165034', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1807213874962817602440880814390', 'Lhash_array': ['1807213874962817602440880814390'], 'label': '2-1368-19.7-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1368/2/s/j/577/2'}