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lfunc_lfunctions • Show schema
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{'Lhash': '1368772716051910451765951799597', 'a10': [1.1375196826253364, -1.9702418849167072], 'a2': [-0.8889851265776415, 1.5397674064055247], 'a3': [1.1557250612421879, 1.290077355361585], 'a4': [-0.5805891105525306, -1.0056098377982068], 'a5': [-1.279571107116817, 0.0], 'a6': [-3.013841453384945, 0.6326881990156821], 'a7': [0.6577611525768807, 1.1392757355082217], 'a8': [-1.4914001705739992, 0.0], 'a9': [-0.3285991656334823, 2.981949461064855], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.1557250612421879, -1.290077355361585]]], [19, [[1.0, 0], [-3.11088848625073, 3.053256102280423]]]], 'bad_primes': [3, 19], 'central_character': '171.121', 'coefficient_field': 'CDF', 'conductor': 171, 'conductor_radical': 57, 'conjugate': '3746249521933569892673050747087', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8889851265776415, 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'7.54716545712844921365674866570605', '8.285468355230217303002537146876775', '9.376511642780686241522517726602917', '10.34988407143960343153285619410242', '11.42426070914637046203425234396902', '12.15081228976354258503329819212030'], 'prelabel': '2-171-171.121-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': -0.8665573959538045, 'root_number': '-0.9134057776076832 - 0.4070502247056296*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.433278697977', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.07977128382653303513199561404', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.68999897758983145279848865285', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.91245971269105548870939262201', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'bad_primes': [3, 19], 'central_character': '171.121', 'conductor': 171, 'conductor_radical': 57, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/171/2/g/c/121/4'], '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': '2-171-171.121-c1-0-2', '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': '2-171-171.121-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': -0.43327869797690227, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.07977128382653303513199561404', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1368772716051910451765951799597', 'Lhash_array': ['1368772716051910451765951799597'], 'label': '2-171-171.121-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/2/g/c/121/4'}