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lfunc_lfunctions • Show schema
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{'Lhash': '1387031226900849635982344130057', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-1.6730326074756159, 0.9659258262890683], 'a6': [0, 0], 'a7': [0.6339745962155614, 0.36602540378443865], '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': '2592.1727', 'coefficient_field': 'CDF', 'conductor': 2592, 'conductor_radical': 6, 'conjugate': '263356310536143016579694127161', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.6730326074756159, -0.9659258262890683], [2.5, -4.330127018922194]], [[1.0, 0], [-0.6339745962155614, -0.36602540378443865], [3.5, 6.06217782649107]], [[1.0, 0], [2.6389584337646843, -4.570810086342821], [-5.5, -9.526279441628825]], [[1.0, 0], [2.232050807568877, 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'root_analytic_conductor': 4.549420205247685, 'root_angle': 0.5555555555555556, 'root_number': '-0.1736481776669303488517166267693147960003756771840693873 + 0.9848077530122080593667430245895230136706432517198424188*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2777777777777778', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.09417470922281486472975426559', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.51739347473293342513889045653', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.45329595377975553460451565254', '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': '36.11', 'conductor': 2592, 'conductor_radical': 6, 'degree': 2, 'index': 28, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2592/2/s/f/1727/1'], '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': '2-2592-36.11-c1-0-28', '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': '2-2592-36.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.549420205247685, 'root_angle': 0.2777777777777778, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.09417470922281486472975426559', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1387031226900849635982344130057', 'Lhash_array': ['1387031226900849635982344130057'], 'label': '2-2592-36.11-c1-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2592/2/s/f/1727/1'}