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lfunc_lfunctions • Show schema
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{'Lhash': '3393174758332181209228426933713', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-8.800725486692274, -6.394101343382615], 'a4': [0.0, 0.0], 'a5': [10.298241745954636, -31.69472908337552], 'a6': [0.0, 0.0], 'a7': [-1.5459198868356292, -2.1277761827374024], 'a8': [0.0, 0.0], 'a9': [11.53786055829686, 35.50988349449392], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.096556751378303, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [79.02950380744156, -91.62607449819937]]]], 'bad_primes': [2, 11], 'central_character': '88.17', 'coefficient_field': 'CDF', 'conductor': 88, 'conductor_radical': 22, 'conjugate': '298990129188255973638611868123', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [8.800725486692274, 6.394101343382615], [25.030376544370743, 77.03557781990745]], [[1.0, 0], [-10.298241745954636, 31.69472908337552], [-505.63562148434215, -367.3657826827957]], 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-1.820503574453389], 'positive_zeros': ['2.67674291143101243875243235629574', '4.47308108618944993512748577511682', '5.93989391974507656994998948280968', '6.73841641326109616841658384257370', '8.556402500216418568869901125849528', '10.07390639614534766251970692187831', '10.96467519905888043071627994110658', '11.25276307557937655437547704958170', '13.06254839130217056579806588578523', '14.02022495872661873421983318672710'], 'prelabel': '2-88-11.6-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0160498589012588, 'root_angle': -0.8804510870179129, 'root_number': '-0.9302972330553585 - 0.3668065677840896*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.440225543509', 'prec': 50}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.67674291143101243875243235630', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.47308108618944993512748577512', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.93989391974507656994998948281', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.096556751378303, 'bad_primes': [2, 11], 'central_character': '11.6', 'conductor': 88, 'conductor_radical': 22, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/88/5/j/a/17/3'], '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': '2-88-11.6-c4-0-10', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-88-11.6-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0160498589012588, 'root_angle': -0.44022554350895643, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '2.67674291143101243875243235630', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3393174758332181209228426933713', 'Lhash_array': ['3393174758332181209228426933713'], 'label': '2-88-11.6-c4-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/88/5/j/a/17/3'}