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lfunc_lfunctions • Show schema
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{'Lhash': '3493000534300185610487881202185', 'a10': [0.7320508075688773, 0.0], 'a2': [0.7320508075688773, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.4641016151377546, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-4.732050807568878, 0.0], 'a8': [-2.5358983848622456, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.233941281861857, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 5], 'central_character': '405.1', 'coefficient_field': 'CDF', 'conductor': 405, 'conductor_radical': 15, 'conjugate': '3493000534300185610487881202185', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7320508075688773, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [4.732050807568878, 0], [7.0, 0]], [[1.0, 0], [5.732050807568878, 0], [11.0, 0]], [[1.0, 0], [-1.4641016151377546, 0], [13.0, 0]], [[1.0, 0], [2.732050807568877, 0], [17.0, 0]], [[1.0, 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'8.113279120425039489990623479180938', '9.160920829589346233820277538329409', '9.891659987097994186587409226243869', '10.53395455354729580116053469386380'], 'prelabel': '2-405-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7983162352216746, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.75549156342552231674726398882', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.61864026751503349114017566624', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.05003835867806828695676183738', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.233941281861857, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 405, 'conductor_radical': 15, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/405/2/a/g/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': '2-405-1.1-c1-0-14', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-405-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7983162352216746, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.75549156342552231674726398882', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3493000534300185610487881202185', 'Lhash_array': ['3493000534300185610487881202185'], 'label': '2-405-1.1-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/405/2/a/g/1/2'}