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lfunc_lfunctions • Show schema
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{'Lhash': '2677126420310971259520667012882', 'a10': [-2.4422375322738614, -0.6587104642644401], 'a2': [0.9983509469272087, 1.0016463381700877], 'a3': [1.2660963944586847, -1.1819475114990168], 'a4': [-0.006590773539091228, 1.9999891403965564], 'a5': [-1.549002538705787, 0.8943170326971999], 'a6': [2.4479019311111907, 0.08818239995659108], 'a7': [2.635730879701317, -0.2300494072779199], 'a8': [-2.0098617038618865, 1.9900894279778973], 'a9': [0.206000160122563, -2.99291896549664], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9983509469272087, -1.0016463381700877]]], [3, [[1.0, 0], [-1.2660963944586847, 1.1819475114990168]]], [7, [[1.0, 0], [-2.635730879701317, 0.2300494072779199]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.101', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': 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'3.80947849295740081158958077562549', '4.53919762110128336297863305947159', '5.78545036172197569130438493890745', '7.893489665413150228044260716058040', '8.539603392578470780454986392744393', '10.01477565215201327251650852176702', '10.63172094506065280543742059472166', '11.85208933131357686534552566192024', '12.51007475368583402931652105667646'], 'prelabel': '2-168-168.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': -0.22221408311380592, 'root_number': '0.7660608787955238 - 0.6427680219013931*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.111107041557', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.11188037131759971268282908547', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.80947849295740081158958077563', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.53919762110128336297863305947', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.341486753957511, 'bad_primes': [2, 3, 7], 'central_character': '168.101', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/ba/c/101/18'], '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': '2-168-168.101-c1-0-17', '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': '2-168-168.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': -0.11110704155690296, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.11188037131759971268282908547', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2677126420310971259520667012882', 'Lhash_array': ['2677126420310971259520667012882'], 'label': '2-168-168.101-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/ba/c/101/18'}