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lfunc_lfunctions • Show schema
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{'Lhash': '1776261081742383065277903162269', 'a10': [5.302775637731995, 0.0], 'a2': [2.302775637731995, 0.0], 'a3': [0.0, 0.0], 'a4': [3.302775637731995, 0.0], 'a5': [2.302775637731995, 0.0], 'a6': [0.0, 0.0], 'a7': [0.3027756377319947, 0.0], 'a8': [3.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20.769089565735037, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 17], 'central_character': '2601.1', 'coefficient_field': 'CDF', 'conductor': 2601, 'conductor_radical': 51, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.302775637731995, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.302775637731995, 0], [5.0, 0]], [[1.0, 0], [-0.3027756377319947, 0], [7.0, 0]], [[1.0, 0], [-3.0, 0], [11.0, 0]], [[1.0, 0], [3.302775637731995, 0], [13.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-5.908326913195984, 0], [19.0, 0]], [[1.0, 0], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 64, 'label': '2-51e2-1.1-c1-0-64', 'leading_term': '5.93920210004737274162964255250', '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/2601/2/a/s/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [5.939202100047373, 5.932450785690337, 5.911891652871145, 5.876630886454811, 5.825249477165874, 5.755903142786637, 5.666451024708769, 5.554604038161133, 5.418083478596405, 5.254781120906159, 5.062913248859287, 4.8411624710239884, 4.588802546762745, 4.3058026055023655, 3.9929080451771832, 3.651696069621538, 3.2846043397836056, 2.894931652041709, 2.4868099927331166, 2.06514780682748, 1.6355448940445958, 1.204180019963628, 0.7776730968187334, 0.3629246280281144, -0.03306400979283939, -0.4033849932977737, 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'5.52491560982247755862769139269112', '6.44395620868282157481517796074622', '6.88429159324680615843438523452335', '7.86855162062521171114478256306760', '9.087462202229563370555152421885801'], 'prelabel': '2-51e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.5573116599301216, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.40122292485214995029027481810', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.48005351212767141663109881742', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.21452038377598959743896610138', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 20.769089565735037, 'bad_primes': [3, 17], 'central_character': '1.1', 'conductor': 2601, 'conductor_radical': 51, 'degree': 2, 'index': 64, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2601/2/a/s/1/2'], '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': '2-51e2-1.1-c1-0-64', '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': '2-51e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.5573116599301216, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.40122292485214995029027481810', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1776261081742383065277903162269', 'Lhash_array': ['1776261081742383065277903162269'], 'label': '2-51e2-1.1-c1-0-64', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2601/2/a/s/1/2'}