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lfunc_lfunctions • Show schema
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{'Lhash': '975384207969164802393254909028', 'a10': [-0.1396285407391647, -0.08973381443201972], 'a2': [0.14231483827328514, 0.9898214418809327], 'a3': [-0.9096319953545183, -0.41541501300188644], 'a4': [-0.9594929736144974, 0.28173255684142967], 'a5': [-0.10869166678020684, 0.1254368702336327], 'a6': [0.28173255684142967, -0.9594929736144974], 'a7': [-0.9037976752256244, -2.486594008328814], 'a8': [-0.41541501300188644, -0.9096319953545183], 'a9': [0.6548607339452851, 0.7557495743542583], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.713548835255689, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.14231483827328514, -0.9898214418809327]]], [3, [[1.0, 0], [0.9096319953545183, 0.41541501300188644]]], [7, [[1.0, 0], [0.9037976752256244, 2.486594008328814]]], [23, [[1.0, 0], [4.730083811972495, 0.791395685934507]]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '966.181', 'coefficient_field': 'CDF', 'conductor': 966, 'conductor_radical': 966, 'conjugate': '1204311927879393782210302432376', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.14231483827328514, -0.9898214418809327]], [[1.0, 0], [0.9096319953545183, 0.41541501300188644]], [[1.0, 0], [0.10869166678020684, -0.1254368702336327], [-0.7115741913664257, -4.949107209404664]], [[1.0, 0], [0.9037976752256244, 2.486594008328814]], [[1.0, 0], [4.0937136602733855, 0.5885871661780252], [10.554422709759471, 3.0990581252557265]], [[1.0, 0], [3.0296341258926023, -4.714202718891792], [-5.400395169024524, -11.82521593960874]], [[1.0, 0], [-7.669483116662927, -2.2519634301957496], [14.30131005813008, 9.190893896745159]], [[1.0, 0], [-7.920165186293045, 2.3255703271437724], [15.983817123792441, -10.272175531656353]], [[1.0, 0], [4.730083811972495, 0.791395685934507]], [[1.0, 0], [-5.413742560352531, -1.5896182416674876], [24.396352452104253, 15.67858370621233]], [[1.0, 0], [-5.534303142069213, 2.5274315585425753], [20.300682752303835, 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[-32.817786027149026, -71.86092763300695]], [[1.0, 0], [-0.17670950301134053, -0.20393363773790008], [-11.812131576682667, 82.15517967611741]], [[1.0, 0], [-0.5134630087188147, 1.1243271584879118], [-58.28260532113037, -67.26171211752899]], [[1.0, 0], [7.869346130855435, -9.081709561375579], [-13.804539312508659, -96.01267986245047]], [[1.0, 0], [-5.274910930444397, 4.5707363399553875], [14.373798665601798, -99.9719656299742]], [[1.0, 0], [0.8813603772677879, -6.129996070885369], [-98.82777628229323, -29.01845335466726]], [[1.0, 0], [-1.4934351441254838, 0.6820289776334991], [70.07009853214551, -80.86520445590564]], [[1.0, 0], [-4.488110748972845, 15.285101504498494], [-91.69663507859875, -58.929849102660135]], [[1.0, 0], [17.69110196380891, -2.543596459247568], [108.4227060184382, -31.835778923081556]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-966-161.20-c1-0-9', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/966/2/s/b/181/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.1372735627681296, 1.0606799983321735, 0.9473667605535336, 0.7935638073830336, 0.5945264464606432, 0.34679604606345876, 0.05027103893650743, -0.29020409227922717, -0.6638915280235536, -1.0539477069237189, -1.4380096863626826, -1.789611026698677, -2.0803975705992777, -2.283022585546375, -2.3744898073080423, -2.339600262838036, -2.1740664321521463, -1.886807918680774, -1.500956072317659, -1.0531841714852026, -0.5911479617218262, -0.16905883816287606, 0.15830509846699328, 0.34255347596026914, 0.348753608191943, 0.16160067605141937, -0.21035941462528768, -0.733370099463188, -1.350578062124596, -1.987774680011356, -2.5623600485831894, -2.994543236560846, -3.2192855126207203, -3.1971620720685774, -2.922249463295184, -2.4253947785704564, 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'rational': False, 'root_analytic_conductor': 2.777327642763037, 'root_angle': -0.28983728686180127, 'root_number': '0.6133108837327209 - 0.7898416043074642*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.144918643431', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.76944246923683498288344327130', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.68383037634162488262130768348', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.18655954025465735393651070496', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.713548835255689, 'bad_primes': [2, 3, 7, 23], 'central_character': '161.20', 'conductor': 966, 'conductor_radical': 966, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/966/2/s/b/181/5'], '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': '2-966-161.20-c1-0-9', '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': '2-966-161.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.777327642763037, 'root_angle': -0.14491864343090063, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.76944246923683498288344327130', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '975384207969164802393254909028', 'Lhash_array': ['975384207969164802393254909028'], 'label': '2-966-161.20-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/966/2/s/b/181/5'}