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lfunc_lfunctions • Show schema
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{'Lhash': '2068210972986185472815328591222', 'a10': [-1.7915787619285775, -1.7856845128927619], 'a2': [-0.3682757009993502, -1.3654204510162564], 'a3': [-1.2660963944586847, 1.1819475114990168], 'a4': [-1.7287460161068744, 1.0057023475137215], 'a5': [1.549002538705787, -0.8943170326971999], 'a6': [2.0801278414305515, 1.2934713616100957], '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], [0.3682757009993502, 1.3654204510162564]]], [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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'6.40239096748176418390966532564139', '7.71434399557879466739818334484805', '8.447847576626659248205386013366490', '10.00877531347115593558810681920304', '10.77375963711578589155068673091951', '12.00476121270336926694625014657099', '13.13729057235427291174042218295931'], 'prelabel': '2-168-168.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.2746390486279316, 'root_number': '0.6503099021979993 + 0.7596690273423212*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.137319524314', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.63153078033791186569497763837', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.53545579427287860850171755716', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.82168197705163954869434291099', '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': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/ba/c/101/10'], '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-c1-0-9', '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': 0.1373195243139658, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.63153078033791186569497763837', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2068210972986185472815328591222', 'Lhash_array': ['2068210972986185472815328591222'], 'label': '2-168-168.101-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/ba/c/101/10'}