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lfunc_lfunctions • Show schema
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{'Lhash': '496970838801271056384027651798', 'a10': [1.0, 0.0], 'a2': [-1.0, 0.0], 'a3': [0.3472963553338607, 0.0], 'a4': [1.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [-0.3472963553338607, 0.0], 'a7': [0.0, 0.0], 'a8': [-1.0, 0.0], 'a9': [-2.879385241571817, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 43.03936668947015, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 7, 11], 'central_character': '5390.1', 'coefficient_field': 'CDF', 'conductor': 5390, 'conductor_radical': 770, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [-0.3472963553338607, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [6.453363193811355, 0], [13.0, 0]], [[1.0, 0], [2.120614758428183, 0], [17.0, 0]], [[1.0, 0], [-5.901673948046147, 0], [19.0, 0]], [[1.0, 0], 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0], [-4.852044095520924, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-5390-1.1-c1-0-3', 'leading_term': '0.50710607746754300565128980561575', '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/5390/2/a/bv/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [0.507106077467543, 0.4998309180795979, 0.4780011369206833, 0.4416080835205371, 0.3906512607540057, 0.3251582686894178, 0.2452109380585205, 0.1509760501083283, 0.04273881191060114, -0.07906284803129145, -0.2138050921864335, -0.36064792580142324, -0.5185095567042313, -0.6860468257764181, -0.8616429399877061, -1.0434034968759933, -1.229161541269055, -1.4164921447362462, -1.602736745822752, -1.7850372334181208, -1.960379495550507, -2.1256458913389804, -2.277675836142356, 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'4.45552772870677711305824760448258', '5.52947675922019981913683579447075', '5.88657240230911053075473457829407', '7.17209857170854968979685911456568', '7.60098217686892199771428213517613', '7.963216260676677579723784652138468'], 'prelabel': '2-5390-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.560439519534507, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.39204086576521622300986012386', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.02107807957531068283684410538', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.61086464320155678627574999297', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 43.03936668947015, 'bad_primes': [2, 5, 7, 11], 'central_character': '1.1', 'conductor': 5390, 'conductor_radical': 770, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5390/2/a/bv/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': '2-5390-1.1-c1-0-3', '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': '2-5390-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.560439519534507, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.39204086576521622300986012386', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '496970838801271056384027651798', 'Lhash_array': ['496970838801271056384027651798'], 'label': '2-5390-1.1-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5390/2/a/bv/1/2'}