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lfunc_lfunctions • Show schema
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{'Lhash': '767399033763881298066844527726', 'a10': [167.61366394415853, 51.70196812880847], 'a2': [-1.9923877509559706, -4.137235795128709], 'a3': [7.0480662605021385, 10.337614549697971], 'a4': [-3.171274244595153, 3.976652122573574], 'a5': [-25.981508911050273, 28.001407117001055], 'a6': [28.72666806590328, -49.75604862231085], 'a7': [-65.61011830078353, 37.880019462520565], 'a8': [-48.858918759373836, -11.151729372585558], 'a9': [-27.59841359202057, 70.319611003424], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.444908412605307, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[43, [[1.0, 0], [231.1908351832492, 1834.4895196558828]]]], 'bad_primes': [43], 'central_character': '43.12', 'coefficient_field': 'CDF', 'conductor': 43, 'conductor_radical': 43, 'conjugate': '3828454816936418910955136901581', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.9923877509559706, 4.137235795128709], [-9.975836829739736, 12.509303719488477]], 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0.9993899588030701*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.244440486459', 'prec': 50}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.60537109644070520302895717730', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.60790025902589033559666603925', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.37019678762605145055677498833', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.444908412605307, 'bad_primes': [43], 'central_character': '43.12', 'conductor': 43, 'conductor_radical': 43, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/43/5/h/a/12/4'], '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': '2-43-43.12-c4-0-1', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-43-43.12-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1082951436184896, 'root_angle': -0.2444404864593697, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '0.60537109644070520302895717730', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '767399033763881298066844527726', 'Lhash_array': ['767399033763881298066844527726'], 'label': '2-43-43.12-c4-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/43/5/h/a/12/4'}