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lfunc_lfunctions • Show schema
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{'Lhash': '1842552827244522809147878488042', 'a10': [0.480096739310563, 1.3190549504095643], 'a2': [-1.2811871120911893, 1.0750436332248015], 'a3': [1.7118730872773178, 0.2636105708343746], 'a4': [0.13842524751751958, -0.7850485896221904], 'a5': [0.28705833506871925, -0.7886862936675452], 'a6': [-2.4766226027817053, 1.5026037974023632], 'a7': [1.6000037149899613, 2.7712877266615665], 'a8': [-1.005858150184443, -1.7421974213267015], 'a9': [2.8610189338887504, 0.9025356834663538], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.7118730872773178, -0.2636105708343746]]], [19, [[1.0, 0], [4.353068741933908, 0.22537197695796926]]]], 'bad_primes': [3, 19], 'central_character': '171.110', 'coefficient_field': 'CDF', 'conductor': 171, 'conductor_radical': 57, 'conjugate': '2768925658422078823931764432255', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[-1.74018148236928, 9.869059603796293], [-83.63264324994584, -30.439792755984517]], [[1.0, 0], [7.4228199667460375, 8.846172362549623], [-16.843873233692243, 95.52635204218419]], [[1.0, 0], [12.283347445323407, -14.638723447047083], [-17.538465944359967, -99.46558305423301]], [[1.0, 0], [-1.4105457324094637, -0.8143789583108817], [51.5, 89.20061658979718]], [[1.0, 0], [9.039669067374902, -15.6571661083021], [-53.5, -92.66471820493493]], [[1.0, 0], [-2.4372847264479995, -2.9046428289193997], [-18.927651365695407, 107.34404507833068]], [[1.0, 0], [3.3500740355338787, 5.802498438661982], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-171-171.110-c1-0-7', '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/171/2/x/a/110/5', 'plot_delta': {'__RealLiteral__': 0, 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{'__RealLiteral__': 0, 'data': '-0.229525209509', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.45351789121764884643333449734', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.89468709184597404934929994242', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.41400723963763703837540727025', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'bad_primes': [3, 19], 'central_character': '171.110', 'conductor': 171, 'conductor_radical': 57, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/171/2/x/a/110/5'], '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': '2-171-171.110-c1-0-7', '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': '2-171-171.110-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': -0.22952520950857486, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.45351789121764884643333449734', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1842552827244522809147878488042', 'Lhash_array': ['1842552827244522809147878488042'], 'label': '2-171-171.110-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/2/x/a/110/5'}