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lfunc_lfunctions • Show schema
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{'Lhash': '1769027358088762559500236852272', 'a10': [0.0, 0.0], 'a2': [0.15555390873299094, -0.2694272732414724], 'a3': [0.514917304110508, -0.8918629324157945], 'a4': [0.9516059629557766, 1.6482298766249122], 'a5': [0.0, 0.0], 'a6': [-0.1601947986572874, -0.27746553038268834], 'a7': [3.2803831053972643, 0.0], 'a8': [1.2143197433775352, 0.0], 'a9': [0.9697203398551333, 1.67960489776205], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.79289409601082, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-2.423458161492814, 3.62309957625979]]]], 'bad_primes': [5, 19], 'central_character': '475.201', 'coefficient_field': 'CDF', 'conductor': 475, 'conductor_radical': 95, 'conjugate': '2365933094977825733505912281505', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.15555390873299094, 0.2694272732414724], [-1.0, -1.7320508075688772]], [[1.0, 0], [-0.514917304110508, 0.8918629324157945], [-1.5, 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'group': 'GL2', 'index': 13, 'label': '2-475-19.11-c1-0-13', '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/475/2/e/h/201/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.0059924823039523, 1.9670379402395648, 1.9239444754677701, 1.8696853632948462, 1.7948900987298315, 1.6893035829888368, 1.5432703466047648, 1.349094640579375, 1.102225484100516, 0.8022486124735336, 0.453651797030591, 0.0662993764085484, -0.3444703433596439, -0.7582139948270791, -1.1502881510830256, -1.49331981152606, -1.7592139032891614, -1.9215995843770979, -1.9585430626496512, -1.855285613433465, -1.6067120430687394, -1.2192276835864244, -0.711730479340251, -0.1154152545128469, 0.5277583075050603, 1.1679680700945303, 1.7516725538213969, 2.2266887868070078, 2.5477322326644414, 2.6818140479267005, 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'9.444965805474070574207145383345610', '10.12314142471837672138831849051861', '10.90468054882854126873713389159985'], 'prelabel': '2-475-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': -0.046763275873053116, 'root_number': '0.9892279502109887 - 0.1463832726829315*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0233816379365', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.39551652306263623325141105058', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.89784213070802412340675698576', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.38383642057555566271134348057', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.79289409601082, 'bad_primes': [5, 19], 'central_character': '19.11', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/2/e/h/201/4'], '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': '2-475-19.11-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': '2-475-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': -0.023381637936526558, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.39551652306263623325141105058', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1769027358088762559500236852272', 'Lhash_array': ['1769027358088762559500236852272'], 'label': '2-475-19.11-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/e/h/201/4'}