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lfunc_lfunctions • Show schema
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{'Lhash': '2172843787350659568056520088495', 'a10': [0.25243523256499295, 0.710373617042041], 'a2': [1.076384934406965, 0.917276115998729], 'a3': [-0.057470032298109784, 1.73109710744015], 'a4': [0.3172090540365722, 1.974684383904735], 'a5': [0.4616631167973844, 0.26654132475789155], 'a6': [-1.6497539080749024, 1.8106109584313208], 'a7': [0.4891800764564067, -2.6001351604864897], 'a8': [-1.4698917751690275, 2.416488810090054], 'a9': [-2.9933943907753084, -0.19897241335149968], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.076384934406965, -0.917276115998729]]], [3, [[1.0, 0], [0.057470032298109784, -1.73109710744015]]], [7, [[1.0, 0], [-0.4891800764564067, 2.6001351604864897]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.5', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': 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'2.97028377650107347997880534057100', '4.96812585601088954868736165919058', '5.88595628478146647846752194025689', '7.02943276274255629211876095093999', '8.451731252455355338231100529604351', '9.586528964309799800252825392667218', '10.89110380570261216381292345787114', '11.85875857686233172318954170528417', '12.48858267911812478132648830212634'], 'prelabel': '2-168-168.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': -0.5492793298788312, 'root_number': '-0.15419788829291944 - 0.9880399846392879*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.274639664939', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.71407151699329298752400282239', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.97028377650107347997880534057', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.96812585601088954868736165919', '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': '168.5', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/ba/c/5/19'], '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': '2-168-168.5-c1-0-8', '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': '2-168-168.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': -0.2746396649394156, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.71407151699329298752400282239', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2172843787350659568056520088495', 'Lhash_array': ['2172843787350659568056520088495'], 'label': '2-168-168.5-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/ba/c/5/19'}