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lfunc_lfunctions • Show schema
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{'Lhash': '2105668109190162514175009192291', 'a10': [0.0, 0.0], 'a2': [1.7320508075688772, 1.7320508075688772], 'a3': [0.0, 0.0], 'a4': [0.0, 4.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.224744871391589, 1.224744871391589], 'a8': [-3.4641016151377544, 3.4641016151377544], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '225.143', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '3847108413480266539949741802105', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.7320508075688772, -1.7320508075688772], [0, 2.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.224744871391589, -1.224744871391589], [0, -7.0]], [[1.0, 0], [0, 4.242640687119285], [-11.0, 0]], [[1.0, 0], [-3.6742346141747673, -3.6742346141747673], 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-0.2399362490776368, -0.862798063748925], 'positive_zeros': ['1.66107925071076792843919169487374', '3.26372502666141841769547144252083', '4.15381994466599468141242269736053', '5.37386830344088950947249805616889', '6.46803442607228886238515453646410', '7.937585008232601384281466879910011', '9.587809450571857974593435357358818', '10.34555405391366795293905913731452', '11.08795902572862517851959309366224', '12.15666584985147851265214895466057'], 'prelabel': '2-15e2-15.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': -0.5958314243854256, 'root_number': '-0.2965358475850581 - 0.9550217228403819*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.297915712193', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.66107925071076792843919169487', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.26372502666141841769547144252', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.15381994466599468141242269736', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'bad_primes': [3, 5], 'central_character': '15.8', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/2/f/b/143/3'], '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': '2-15e2-15.8-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': '2-15e2-15.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': -0.2979157121927128, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.66107925071076792843919169487', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2105668109190162514175009192291', 'Lhash_array': ['2105668109190162514175009192291'], 'label': '2-15e2-15.8-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/2/f/b/143/3'}