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lfunc_lfunctions • Show schema
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{'Lhash': '2921254015967896275305368152492', 'a10': [3.0862470596386, 0.0], 'a2': [1.627947598334506, 0.0], 'a3': [1.5157396789791941, 0.0], 'a4': [0.6502133829230863, 0.0], 'a5': [1.8957901733422053, 0.0], 'a6': [2.467544770094494, 0.0], 'a7': [1.0, 0.0], 'a8': [-2.1973818815344193, 0.0], 'a9': [-0.7025332255680496, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.4034971008405406, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-1.0, 0]]], [43, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [7, 43], 'central_character': '301.1', 'coefficient_field': 'CDF', 'conductor': 301, 'conductor_radical': 301, 'conjugate': '2921254015967896275305368152492', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.627947598334506, 0], [2.0, 0]], [[1.0, 0], [-1.5157396789791941, 0], [3.0, 0]], [[1.0, 0], [-1.8957901733422053, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.0394774506559057, 0], [11.0, 0]], [[1.0, 0], 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'4.63957400875972780805929890739881', '5.52510228592135476436621685444538', '6.55312224515157899052759050721717', '8.007774977996019585105171975193975', '8.894394786790604777587327560431895', '9.740305323580045169449740344154310', '10.94059916867066879526433161672602', '12.01941127671036390876376254050868'], 'prelabel': '2-301-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5503216120665224, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.30446308741695073081884917481', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.23749117520206814514257971575', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.63957400875972780805929890740', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.4034971008405406, 'bad_primes': [7, 43], 'central_character': '1.1', 'conductor': 301, 'conductor_radical': 301, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/301/2/a/d/1/5'], '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': '2-301-1.1-c1-0-13', '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': '2-301-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5503216120665224, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.30446308741695073081884917481', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2921254015967896275305368152492', 'Lhash_array': ['2921254015967896275305368152492'], 'label': '2-301-1.1-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/301/2/a/d/1/5'}