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lfunc_lfunctions • Show schema
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{'Lhash': '1306879746959512906881167175284', 'a10': [-1.0820706202590524, 1.9568145473631857], 'a2': [0.5406408174555976, 0.8412535328311812], 'a3': [-0.6659930125320146, -0.09575533915442594], 'a4': [-0.41541501300188644, 0.9096319953545183], 'a5': [1.0611656063831891, 1.9682295485611931], 'a6': [-0.27950848936391565, -0.6120382194696252], 'a7': [-1.6232948121353832, 1.4065929616868742], 'a8': [-0.9898214418809327, 0.14231483827328514], 'a9': [-2.4441013130786033, -0.7176528969453273], '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], [-1.0611656063831891, -1.9682295485611931]]], [23, [[1.0, 0], [-2.94656308257576, 3.7838823978027696]]]], 'bad_primes': [2, 5, 23], 'central_character': '230.219', 'coefficient_field': 'CDF', 'conductor': 230, 'conductor_radical': 230, 'conjugate': 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'root_analytic_conductor': 1.355197124587213, 'root_angle': -0.3078625110212195, 'root_number': '-0.3556046082658431 - 0.9346364868653996*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.307862511021', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.03094634020148820241300319803', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.10086161730351728749918577235', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.40633146491352019478964296937', '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': '115.104', 'conductor': 230, 'conductor_radical': 230, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/230/2/j/a/219/9'], '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': '2-230-115.104-c1-0-1', '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': '2-230-115.104-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.355197124587213, 'root_angle': -0.3078625110212195, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.03094634020148820241300319803', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1306879746959512906881167175284', 'Lhash_array': ['1306879746959512906881167175284'], 'factors': ['2-230-115.104-c1-0-1'], 'label': '2-230-115.104-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/230/2/j/a/219/9'}