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lfunc_lfunctions • Show schema
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{'Lhash': '2727777331926175464543776808036', 'a10': [1.527981249763242, -2.6465411576025257], 'a2': [0.8660254037844386, 0.5], 'a3': [0.5, -0.8660254037844386], 'a4': [0.5, 0.8660254037844386], 'a5': [0.0, -3.055962499526484], 'a6': [0.8660254037844386, -0.5], 'a7': [0.8660254037844386, -0.5], 'a8': [0.0, 1.0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.359831950361911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, -0.5]]], [3, [[1.0, 0], [-0.5, 0.8660254037844386]]], [7, [[1.0, 0], [-0.8660254037844386, 0.5]]], [13, [[1.0, 0], [-3.2525345040548452, -1.5559624995264838]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.43', 'coefficient_field': 'CDF', 'conductor': 546, 'conductor_radical': 546, 'conjugate': '1413962800047984834021275886661', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [-0.5, 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4.988765410507838], [29.5, -51.09549882328188]], [[1.0, 0], [-5.772598618719083, -9.998434099323374], [-30.5, 52.827549630850754]], [[1.0, 0], [-4.114096134591229, -2.375274510778245], [33.5, 58.023702053557386]], [[1.0, 0], [3.1778398617589256, -1.8347266996280387], [35.5, -61.48780366869514]], [[1.0, 0], [0, -10.111924999052968], [-73.0, 0]], [[1.0, 0], [4.498434099323374, 0], [79.0, 0]], [[1.0, 0], [0, -7.15868813716776], [-83.0, 0]], [[1.0, 0], [6.844259480985784, 3.9515350537507903], [44.5, 77.07626093681505]], [[1.0, 0], [7.8801578658480285, -4.549611265104106], [48.5, -84.00446416709055]], [[1.0, 0], [-9.426637329598883, 16.32741479939067], [-50.5, -87.4685657822283]], [[1.0, 0], [13.707856339602637, 0], [103.0, 0]], [[1.0, 0], [-1.6573561652729578, 2.870625084490284], [-53.5, -92.66471820493493]], [[1.0, 0], [0, -8.675249144398935], [-109.0, 0]], [[1.0, 0], [-5.6055737646305905, -9.709138565915325], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 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'10.36055270479569596047627452522672', '10.89294340653573189869796428080964'], 'prelabel': '2-546-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.3046166283859224, 'root_number': '0.5759902121919193 + 0.8174565893422768*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.152308314193', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.15183689530463916303899119836', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.13249927276825195201384804925', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.03818256803755228264191672854', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.359831950361911, 'bad_primes': [2, 3, 7, 13], 'central_character': '13.4', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/s/e/43/3'], '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': '2-546-13.4-c1-0-11', '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': '2-546-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.1523083141929612, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.15183689530463916303899119836', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2727777331926175464543776808036', 'Lhash_array': ['2727777331926175464543776808036'], 'label': '2-546-13.4-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/s/e/43/3'}