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lfunc_lfunctions • Show schema
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{'Lhash': '1905070236910845284740401141599', 'a10': [0.0, 0.0], 'a2': [-1.2570684646676455, 2.1773064493969643], 'a3': [0.0, 0.0], 'a4': [-2.160442249723743, -3.7419957433399316], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.25706846466764555, 0.44525564182808686], 'a8': [5.8350214287827775, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.389902136436429, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '675.451', 'coefficient_field': 'CDF', 'conductor': 675, 'conductor_radical': 15, 'conjugate': '153025263318432582801684504925', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.2570684646676455, -2.1773064493969643], [-1.0, -1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.25706846466764555, -0.44525564182808686], [-3.5, -6.06217782649107]], [[1.0, 0], [1.6604422497237432, 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2.321616276742655, 'root_angle': 0.2970397670898315, 'root_number': '0.5952834595234345 + 0.8035157763341124*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.148519883545', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.50283543159909682813111091049', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.73715037349610513840168530819', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.64500975778967013080768340106', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.389902136436429, 'bad_primes': [3, 5], 'central_character': '9.7', 'conductor': 675, 'conductor_radical': 15, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/675/2/e/b/451/1'], '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': '2-675-9.7-c1-0-9', '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': '2-675-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.321616276742655, 'root_angle': 0.14851988354491574, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.50283543159909682813111091049', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1905070236910845284740401141599', 'Lhash_array': ['1905070236910845284740401141599'], 'label': '2-675-9.7-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/675/2/e/b/451/1'}