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lfunc_lfunctions • Show schema
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{'Lhash': '1846788664080583144371266730598', 'a10': [0, 0], 'a2': [1.0, 0], 'a3': [0, 0], 'a4': [1.0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-0.5, -2.598076211353316], 'a8': [1.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.0550355892132, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.5, 2.598076211353316]]]], 'bad_primes': [2, 3, 7], 'central_character': '1134.865', 'coefficient_field': 'CDF', 'conductor': 1134, 'conductor_radical': 42, 'conjugate': '1334400046923595688391705786117', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-2.5, -4.330127018922194]], [[1.0, 0], [0.5, 2.598076211353316]], [[1.0, 0], [-3.0, -5.196152422706632], [-5.5, 9.526279441628825]], [[1.0, 0], [2.5, 4.330127018922194], [-6.5, 11.258330249197702]], [[1.0, 0], [-3.0, 5.196152422706632], [-8.5, 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0.6310461434394039, 0.4285741658754185, 0.1398707216110509, -0.21985537372297728, -0.6297173619370203], 'positive_zeros': ['1.45685937729851190905882712232841', '2.84334288646061969186461333610846', '3.61524966323110508303152505131956', '4.76574011115947488832893584226857', '5.69751939932530624951526541797697', '6.35293121075353093682762361401426', '7.15235118997075856624656702725152', '8.436941407549846736404055352109791', '8.959865939426136703937909115792577', '9.834200577861963653558935819175981'], 'prelabel': '2-1134-63.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.00915861815445, 'root_angle': 0.18187631611433, 'root_number': '0.84115477925641530262327173010861727601929270590995212461 + 0.54079445016946248661107852846796300023826273080488025355*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.090938158057165', 'prec': 57}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.0550355892132, 'bad_primes': [2, 3, 7], 'central_character': '63.25', 'conductor': 1134, 'conductor_radical': 42, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1134/2/e/m/865/1'], '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': '2-1134-63.25-c1-0-20', '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': '2-1134-63.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.00915861815445, 'root_angle': 0.090938158057165, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.45685937729851190905882712233', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1846788664080583144371266730598', 'Lhash_array': ['1846788664080583144371266730598'], 'label': '2-1134-63.25-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1134/2/e/m/865/1'}