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lfunc_lfunctions • Show schema
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{'Lhash': '339625124398515431988125287829', 'a10': [9.340593033237592, 5.177968505603242], 'a2': [-0.7727972762488496, -0.5614700867214965], 'a3': [0.0, 0.0], 'a4': [-2.190168983104983, -6.7406470229340725], 'a5': [-11.097047203457207, 1.3621833078710763], 'a6': [0.0, 0.0], 'a7': [12.483557596416494, 0.0], 'a8': [-4.453573388767297, 13.706689500210913], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.275429751291645, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [11.097047203457207, -1.3621833078710763]]]], 'bad_primes': [3, 5], 'central_character': '225.91', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '1656897268712790251072649864881', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7727972762488496, 0.5614700867214965], [2.4721359549995796, 7.608452130361228]], [[1.0, 0], [0, 0]], [[1.0, 0], [11.097047203457207, 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[-738367.9673071664, 536455.7295655283]], [[1.0, 0], [-433.24842481126655, 0], [1030301.0, 0]], [[1.0, 0], [-25.130630450757373, -77.3441276171311], [-884034.7132123532, 642288.8153817973]], [[1.0, 0], [391.77318413956897, 0], [1225043.0, 0]], [[1.0, 0], [1469.1127035421414, -1067.3728575562977], [400185.96920839377, -1231645.7692411963]], [[1.0, 0], [-879.5670987603727, 639.0429034837022], [445879.6941326285, -1372276.5941927282]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-15e2-25.16-c3-0-3', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/225/4/h/a/91/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.5367960968468952, 0.30639515209540485, 0.040684183364845014, -0.2551311404446552, -0.5749722147670934, -0.9116256540080866, 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'data': '2.66764836370677833630888216609', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.14700704904629098165243374278', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.275429751291645, 'bad_primes': [3, 5], 'central_character': '25.16', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/4/h/a/91/3'], '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': '2-15e2-25.16-c3-0-3', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-15e2-25.16-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': -0.21887863790355697, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.26791698306881162624111726396', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '339625124398515431988125287829', 'Lhash_array': ['339625124398515431988125287829'], 'label': '2-15e2-25.16-c3-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/4/h/a/91/3'}