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lfunc_lfunctions • Show schema
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{'Lhash': '1485955214955549842445631904554', 'a10': [1179.6152422706632, 0], 'a2': [4.898979485566356, -2.8284271247461903], 'a3': [0, 0], 'a4': [16.0, -27.712812921102035], 'a5': [180.59096477329268, 104.26424212507476], 'a6': [0, 0], 'a7': [-2.098076211353316, -3.633974596215561], 'a8': [0, -181.01933598375618], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 37.26876154641587, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-4.898979485566356, 2.8284271247461903]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '162.53', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '1710299194769846077295242613151', 'degree': 2, 'euler_factors': [[[1.0, 0], [-4.898979485566356, 2.8284271247461903]], [[1.0, 0], [0, 0]], [[1.0, 0], [-180.59096477329268, -104.26424212507476], [7812.5, 13531.646934131853]], [[1.0, 0], [2.098076211353316, 3.633974596215561], 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'4.24596428752086627774621266271419', '5.32017911953237524361478373809737', '6.18889200898397756053415332137783', '7.35140603724078099725013795391210', '8.866368955862572969773262757511146', '9.560736258767790082573087378339975', '10.70356160916529237267450467417262', '12.32655160051307051313126627289080'], 'prelabel': '2-162-9.5-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.104814620151529, 'root_angle': 0.027777777777777783, 'root_number': '0.99619469809174553229501040247388804618356267264585097453 + 0.0871557427476581735580642708374735513777011561497026727*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.013888888888888888', 'prec': 67}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.17221197598771822830256787170', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.45796904954714194757540929572', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.24596428752086627774621266271', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 37.26876154641587, 'bad_primes': [2, 3], 'central_character': '9.5', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/7/d/f/53/4'], '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': '2-162-9.5-c6-0-12', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-162-9.5-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.104814620151529, 'root_angle': 0.013888888888888892, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '1.17221197598771822830256787170', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1485955214955549842445631904554', 'Lhash_array': ['1485955214955549842445631904554'], 'label': '2-162-9.5-c6-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/7/d/f/53/4'}