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lfunc_lfunctions • Show schema
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{'Lhash': '1815880638192006257139675024393', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0.27525512860841095, 0.15891862259789113], 'a6': [0, 0], 'a7': [-1.255294939775204, 0.724744871391589], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20.697224203915887, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '2592.863', 'coefficient_field': 'CDF', 'conductor': 2592, 'conductor_radical': 6, 'conjugate': '83696993943859708504766249204', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.27525512860841095, -0.15891862259789113], [2.5, 4.330127018922194]], [[1.0, 0], [1.255294939775204, -0.724744871391589], [3.5, -6.06217782649107]], [[1.0, 0], [0.5481881585886564, 0.9494897427831781], [-5.5, 9.526279441628825]], [[1.0, 0], [1.449489742783178, 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4.549420205247685, 'root_angle': 0.8611111111111112, 'root_number': '-0.9063077870366499632425526567543169832677126251758646809 + 0.4226182617406994361869784896477301815631293011948646235*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4305555555555556', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.43247724401745467803188392050', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.66735245335462995189307142728', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.51383258288459783778970509195', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 20.697224203915887, 'bad_primes': [2, 3], 'central_character': '36.23', 'conductor': 2592, 'conductor_radical': 6, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2592/2/s/h/863/1'], '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': '2-2592-36.23-c1-0-38', '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': '2-2592-36.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.549420205247685, 'root_angle': 0.4305555555555556, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.43247724401745467803188392050', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1815880638192006257139675024393', 'Lhash_array': ['1815880638192006257139675024393'], 'label': '2-2592-36.23-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2592/2/s/h/863/1'}