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lfunc_lfunctions • Show schema
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{'Lhash': '1742137026764447629117324980327', 'a10': [0, 0], 'a2': [0, 0], 'a3': [1.7320508075688772, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [3.4641016151377544, 0], 'a8': [0, 0], 'a9': [3.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.58204824255365, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.7320508075688772, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1200.1199', 'coefficient_field': 'CDF', 'conductor': 1200, 'conductor_radical': 30, 'conjugate': '1815021021509110260562570434764', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.7320508075688772, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.4641016151377544, 0], [7.0, 0]], [[1.0, 0], [0, 0], [11.0, 0]], [[1.0, 0], [0, -2.0], [-13.0, 0]], [[1.0, 0], [0, 0], [17.0, 0]], [[1.0, 0], [0, 3.4641016151377544], [-19.0, 0]], [[1.0, 0], [0, 0], [-23.0, 0]], [[1.0, 0], [0, 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'rational': False, 'root_analytic_conductor': 3.095488368990207, 'root_angle': -0.019083049016233394, 'root_number': '0.998203466991462346676770446829607545710646177019470737745 - 0.05991526087921625076390819376801528600483150139314606220*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.009541524508116697', 'prec': 70}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.37430379195244422809042879405', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.37564078097062930691690106768', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.54688504928705794489292021329', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.58204824255365, 'bad_primes': [2, 3, 5], 'central_character': '60.59', 'conductor': 1200, 'conductor_radical': 30, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1200/2/o/i/1199/4'], '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': '2-1200-60.59-c1-0-24', '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': '2-1200-60.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.095488368990207, 'root_angle': -0.009541524508116697, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.37430379195244422809042879405', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1742137026764447629117324980327', 'Lhash_array': ['1742137026764447629117324980327'], 'label': '2-1200-60.59-c1-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1200/2/o/i/1199/4'}