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lfunc_lfunctions • Show schema
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{'Lhash': '1607567745356226280730863894336', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-2.0, -2.23606797749979], 'a4': [0, 0], 'a5': [0, -2.23606797749979], 'a6': [0, 0], 'a7': [2.0, 0], 'a8': [0, 0], 'a9': [-1.0, 8.94427190999916], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.158105378588505, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [2.0, 2.23606797749979]]], [5, [[1.0, 0], [0, 2.23606797749979]]]], 'bad_primes': [2, 3, 5], 'central_character': '960.641', 'coefficient_field': 'CDF', 'conductor': 960, 'conductor_radical': 30, 'conjugate': '479533928998644874135592841045', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.0, 2.23606797749979]], [[1.0, 0], [0, 2.23606797749979]], [[1.0, 0], [-2.0, 0], [49.0, 0]], [[1.0, 0], [0, -13.416407864998739], [-121.0, 0]], [[1.0, 0], [8.0, 0], [169.0, 0]], [[1.0, 0], [0, 13.416407864998739], [-289.0, 0]], [[1.0, 0], [-34.0, 0], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 45, 'label': '2-960-3.2-c2-0-45', 'leading_term': '0.99693871615444536496136877841727502243077479662923466', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/960/3/l/a/641/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.9969387161544454, 1.1425236695891652, 1.2779279681804776, 1.4013783974419447, 1.5110705148818215, 1.6051647875729307, 1.6817915827617105, 1.7390658563785615, 1.775111879503242, 1.7880978354314592, 1.7762796334353754, 1.7380528369462926, 1.672011204896167, 1.577010001420449, 1.4522319436995599, 1.297253431409605, 1.1121085349590156, 0.8973481152155642, 0.6540914079575239, 0.3840674362930546, 0.08964371907826138, -0.22616007171571278, -0.5596755821487508, -0.9066080963718403, -1.2620789812240376, 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'6.68928295667757949413786333595963', '7.54612093480690035841000551629595', '8.633970359932460989212575507849968', '9.456582575263715267585242820110012', '10.24782610220659871149923157772363'], 'prelabel': '2-960-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.114499523764618, 'root_angle': 0.7677204728012301, 'root_number': '-0.74535599249992989880305788957709207848020611987050858 + 0.66666666666666666666666666666666666666666666666666667*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.38386023640061506', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.26814734680581366092497485280', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.15944751268388825804045014826', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.73107779751504392107274286673', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.158105378588505, 'bad_primes': [2, 3, 5], 'central_character': '3.2', 'conductor': 960, 'conductor_radical': 30, 'degree': 2, 'index': 45, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/960/3/l/a/641/1'], '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': '2-960-3.2-c2-0-45', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-960-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.114499523764618, 'root_angle': 0.38386023640061506, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.26814734680581366092497485280', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1607567745356226280730863894336', 'Lhash_array': ['1607567745356226280730863894336'], 'label': '2-960-3.2-c2-0-45', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/960/3/l/a/641/1'}