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lfunc_lfunctions • Show schema
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{'Lhash': '819990215910617449993862210377', 'a10': [-0.8591940429425314, 0.3750014044533409], 'a2': [-0.565708717888457, -1.296137973560299], 'a3': [-1.4023124823740631, -1.0166217102629145], 'a4': [-1.3599472930099963, 1.466473102458679], 'a5': [0.0, -0.6628877947171417], 'a6': [-0.5243816069347685, 2.392702223493034], 'a7': [0.0, 4.602966929350501], 'a8': [2.67008551482604, 0.9330827099009835], 'a9': [0.9329605964442137, 2.851242628308306], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.2038710957873398, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.565708717888457, 1.296137973560299]]], [3, [[1.0, 0], [1.4023124823740631, 1.0166217102629145]]], [23, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 23], 'central_character': '276.47', 'coefficient_field': 'CDF', 'conductor': 276, 'conductor_radical': 138, 'conjugate': '2040114617938838109765667333309', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'z2': {'__RealLiteral__': 0, 'data': '3.86751924330338071703542910833', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.75911786388651231786771409820', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.2038710957873398, 'bad_primes': [2, 3, 23], 'central_character': '12.11', 'conductor': 276, 'conductor_radical': 138, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/276/2/c/a/47/7'], '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': '2-276-12.11-c1-0-4', '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': '2-276-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.484544070005111, 'root_angle': -0.031160480831999716, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.64685822399562259874930906415', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '819990215910617449993862210377', 'Lhash_array': ['819990215910617449993862210377'], 'label': '2-276-12.11-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/276/2/c/a/47/7'}