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lfunc_lfunctions • Show schema
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{'Lhash': '487375143885636754688386158988', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.2928932188134525, -1.7071067811865475], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.0, 2.0], 'a8': [0.0, 0.0], 'a9': [-2.8284271247461903, 1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.791024121276825, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.2928932188134525, 1.7071067811865475]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '600.593', 'coefficient_field': 'CDF', 'conductor': 600, 'conductor_radical': 30, 'conjugate': '2291038336704381765357252334113', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.2928932188134525, 1.7071067811865475]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.0, -2.0], [0, -7.0]], [[1.0, 0], [0, -5.656854249492381], [-11.0, 0]], [[1.0, 0], [0, 0], [0, 13.0]], [[1.0, 0], [2.8284271247461903, 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'4.69356754640700969671639254612201', '6.03378294820230431158942823605502', '6.50791660362568492561762371583541', '8.057712679896400733452429619944810', '8.791832748349670179108095277248027', '9.688495470443984327166757642218573', '10.52112988028441136435944972993360'], 'prelabel': '2-600-15.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.188840816797061, 'root_angle': -0.48029491515947975, 'root_number': '0.06186581765581935 - 0.9980844756861901*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.24014745758', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.38447119718784428726770885984', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.87984528571417189245894499157', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.78386079499813411511917271885', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.791024121276825, 'bad_primes': [2, 3, 5], 'central_character': '15.8', 'conductor': 600, 'conductor_radical': 30, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/600/2/r/a/593/2'], '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': '2-600-15.8-c1-0-1', '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': '2-600-15.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.188840816797061, 'root_angle': -0.24014745757973988, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.38447119718784428726770885984', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '487375143885636754688386158988', 'Lhash_array': ['487375143885636754688386158988'], 'label': '2-600-15.8-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/600/2/r/a/593/2'}