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lfunc_lfunctions • Show schema
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{'Lhash': '1880261973818490204076434533456', 'a10': [0.0, 1.9567255714311302], 'a2': [1.0, 0.0], 'a3': [1.2508361505002776, -1.198085524744226], 'a4': [1.0, 0.0], 'a5': [0.0, 1.9567255714311302], 'a6': [1.2508361505002776, -1.198085524744226], 'a7': [1.989399020155899, 1.7442165973877066], 'a8': [1.0, 0.0], 'a9': [0.12918215079670595, -2.997217371482345], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.372062081298178, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [-1.2508361505002776, 1.198085524744226]]], [7, [[1.0, 0], [-1.989399020155899, -1.7442165973877066]]], [19, [[1.0, 0], [-4.358767920406826, -0.03379668670676678]]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '798.107', 'coefficient_field': 'CDF', 'conductor': 798, 'conductor_radical': 798, 'conjugate': '2221834650696189544965043005689', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], 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'6.84274090164851345495637521119510', '7.973631088741487586722025556220204', '8.349664645731497928100798277370212', '9.507830331468551617811794193545640', '10.25517334264926653485318063390710'], 'prelabel': '2-798-399.107-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.524294372948246, 'root_angle': -0.000562468512929588, 'root_number': '0.9999984387729478 - 0.0017670460285079076*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.000281234256465', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.48326516271910058160201566245', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.93296969465563985836490093849', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.97418188584524573852404507310', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.372062081298178, 'bad_primes': [2, 3, 7, 19], 'central_character': '399.107', 'conductor': 798, 'conductor_radical': 798, 'degree': 2, 'index': 33, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/798/2/p/d/107/18'], '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': '2-798-399.107-c1-0-33', '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': '2-798-399.107-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.524294372948246, 'root_angle': -0.000281234256464794, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.48326516271910058160201566245', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1880261973818490204076434533456', 'Lhash_array': ['1880261973818490204076434533456'], 'label': '2-798-399.107-c1-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/798/2/p/d/107/18'}