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lfunc_lfunctions • Show schema
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{'Lhash': '650163755334078255925281772990', 'a10': [-1.2606045583465275, 0.0], 'a2': [-0.44952133130070154, 0.0], 'a3': [-2.7428168755280757, 0.0], 'a4': [-1.797930572705645, 0.0], 'a5': [2.8043264480885384, 0.0], 'a6': [1.2329546934014113, 0.0], 'a7': [-4.111214693248016, 0.0], 'a8': [1.7072508072302774, 0.0], 'a9': [4.523044412681596, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.20770826531158, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [-1.0, 0]]], [17, [[1.0, 0], [-1.0, 0]]], [43, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [11, 17, 43], 'central_character': '8041.1', 'coefficient_field': 'CDF', 'conductor': 8041, 'conductor_radical': 8041, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.44952133130070154, 0], [2.0, 0]], [[1.0, 0], [2.7428168755280757, 0], [3.0, 0]], [[1.0, 0], [-2.8043264480885384, 0], [5.0, 0]], [[1.0, 0], [4.111214693248016, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], 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['0.51288876857473341568969339535676', '1.29140250294908686535201234981259', '2.65001746044862002728902649629324', '3.56851626814884824616347707299494', '4.60308421214670522934742495406348', '5.34648031743419863462328576393578', '5.56113100735063581701775785584211', '6.45557845283797138977813082306744', '6.83816275949479842102712961805435', '7.63112849685945205289844280400099'], 'prelabel': '2-8041-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.012971250747851, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.51288876857473341568969339536', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.29140250294908686535201234981', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.65001746044862002728902649629', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.20770826531158, 'bad_primes': [11, 17, 43], 'central_character': '1.1', 'conductor': 8041, 'conductor_radical': 8041, 'degree': 2, 'index': 108, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8041/2/a/j/1/34'], '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': '2-8041-1.1-c1-0-108', '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': '2-8041-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.012971250747851, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.51288876857473341568969339536', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '650163755334078255925281772990', 'Lhash_array': ['650163755334078255925281772990'], 'label': '2-8041-1.1-c1-0-108', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8041/2/a/j/1/34'}