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lfunc_lfunctions • Show schema
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{'Lhash': '3526710451615623873795805635945', 'a10': [-2.1189483181765425, 0.7141834672525], 'a2': [0.5406408174555976, -0.8412535328311812], 'a3': [2.161510425034504, -0.31077828136381064], 'a4': [-0.41541501300188644, -0.9096319953545183], 'a5': [-1.7463993158009175, -1.3964560250040414], 'a6': [0.9071574360049418, -1.9863977053956807], 'a7': [-0.2823028976319057, -0.24461685326924565], 'a8': [-0.9898214418809327, -0.14231483827328514], 'a9': [1.6970652565219055, -0.4983033195600768], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5406408174555976, 0.8412535328311812]]], [5, [[1.0, 0], [1.7463993158009175, 1.3964560250040414]]], [23, [[1.0, 0], [0.7107404539978741, -4.742873391421164]]]], 'bad_primes': [2, 5, 23], 'central_character': '230.209', 'coefficient_field': 'CDF', 'conductor': 230, 'conductor_radical': 230, 'conjugate': 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'root_angle': 0.21549121842387087, 'root_number': '0.21513012168401366 + 0.9765853934726966*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.215491218424', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.78208399931390440529814665214', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.66852683131047450126845339360', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.88974204437731915107702601659', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'bad_primes': [2, 5, 23], 'central_character': '115.94', 'conductor': 230, 'conductor_radical': 230, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/230/2/j/a/209/11'], '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': '2-230-115.94-c1-0-11', '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': '2-230-115.94-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.355197124587213, 'root_angle': 0.21549121842387087, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.78208399931390440529814665214', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3526710451615623873795805635945', 'Lhash_array': ['3526710451615623873795805635945'], 'factors': ['2-230-115.94-c1-0-11'], 'label': '2-230-115.94-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/230/2/j/a/209/11'}