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lfunc_lfunctions • Show schema
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{'Lhash': '2224010501494481329587760244027', 'a10': [0, 0], 'a2': [1.7320508075688772, -1.0], 'a3': [-8.226237104181658, -4.749420206516968], 'a4': [2.0, -3.4641016151377544], 'a5': [0, 0], 'a6': [-18.99768082606787, 0], 'a7': [14.659705320415306, -11.317819574396262], 'a8': [0, -8.0], 'a9': [31.61398459614336, 54.75702755022015], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20.650668502009225, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.7320508075688772, 1.0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-14.659705320415306, 11.317819574396262]]]], 'bad_primes': [2, 5, 7], 'central_character': '350.249', 'coefficient_field': 'CDF', 'conductor': 350, 'conductor_radical': 70, 'conjugate': '794121646340290490241003042323', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.7320508075688772, 1.0]], [[1.0, 0], [8.226237104181658, 4.749420206516968], [13.5, 23.382685902179844]], [[1.0, 0], [0, 0]], [[1.0, 0], 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0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 26, 'label': '2-350-35.4-c3-0-26', 'leading_term': '1.588264720272251685130407818539683099260227777096316565', '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/350/4/j/j/249/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [1.5882647202722517, 1.7856977088115205, 1.9785011314142988, 2.164244680753996, 2.3404511458757686, 2.5045950776360066, 2.6541064204829192, 2.786380206450627, 2.8987931629877823, 2.9887278046705887, 3.053604270158434, 3.0909198399671802, 3.0982957372067275, 3.073530481047955, 3.014658739332302, 2.9200143198877497, 2.7882956570044284, 2.6186318974201384, 2.410647476565641, 2.1645229085169, 1.881049400123465, 1.5616748491731598, 1.2085388059319722, 0.8244940739110698, 0.4131128049197814, 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'9.091466325425437074596881301312667', '9.631348546287717434183420862360239', '10.98743036377817048951878604755762', '11.68329633273827898711513566432742'], 'prelabel': '2-350-35.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.544300661488985, 'root_angle': 0.9966480504822834, 'root_number': '-0.999944555218665693549720942219422860421369304804179256256 + 0.0105302653596590666116434099663193946602281715363303438*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4983240252411417', 'prec': 60}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.75443493742997297035414299217', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.07216687548599378693197317639', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.65557865122520399148933885306', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 20.650668502009225, 'bad_primes': [2, 5, 7], 'central_character': '35.4', 'conductor': 350, 'conductor_radical': 70, 'degree': 2, 'index': 26, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/350/4/j/j/249/5'], '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': '2-350-35.4-c3-0-26', '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': '2-350-35.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.544300661488985, 'root_angle': 0.4983240252411417, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.75443493742997297035414299217', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2224010501494481329587760244027', 'Lhash_array': ['2224010501494481329587760244027'], 'label': '2-350-35.4-c3-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/350/4/j/j/249/5'}