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lfunc_lfunctions • Show schema
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{'Lhash': '2433540269728505158170899671964', 'a10': [-0.44235772511351856, 1.343249657745124], 'a2': [-1.343249657745124, -0.44235772511351856], 'a3': [0.9012780559847996, 0.0], 'a4': [1.6086392860647856, 1.188393725719291], 'a5': [0.0, -1.0], 'a6': [-1.2106414402347727, -0.39868731054017037], 'a7': [0.0, 0.0], 'a8': [-1.6351090253935194, -2.3079034804507432], 'a9': [-2.1876978658002604, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.8253393980854815, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.343249657745124, 0.44235772511351856]]], [5, [[1.0, 0], [0, 1.0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5, 7], 'central_character': '980.391', 'coefficient_field': 'CDF', 'conductor': 980, 'conductor_radical': 70, 'conjugate': '329219756852101522864103436657', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.343249657745124, 0.44235772511351856]], [[1.0, 0], [-0.9012780559847996, 0], [3.0, 0]], [[1.0, 0], 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'positive_zeros': ['1.91972478006981381192670588866209', '2.66734299043994615065085444123639', '4.11699246518784113650723905306332', '5.39747800383280773219734209299567', '6.51211872700784935517209440818626', '7.05575178018961337416718775091625', '8.013441431276351695386297157808189', '8.778836768592075447162140232340842', '9.343742423631022788231540181766428', '10.33928795614909088116921128682735'], 'prelabel': '2-980-28.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.797380810344827, 'root_angle': 0.9297155226541142, 'root_number': '-0.9757214150026496 + 0.2190153426251848*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.464857761327', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.91972478006981381192670588866', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.66734299043994615065085444124', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.11699246518784113650723905306', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.8253393980854815, 'bad_primes': [2, 5, 7], 'central_character': '28.27', 'conductor': 980, 'conductor_radical': 70, 'degree': 2, 'index': 69, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/980/2/g/a/391/6'], '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': '2-980-28.27-c1-0-69', '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': '2-980-28.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.797380810344827, 'root_angle': 0.4648577613270571, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.91972478006981381192670588866', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2433540269728505158170899671964', 'Lhash_array': ['2433540269728505158170899671964'], 'label': '2-980-28.27-c1-0-69', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/980/2/g/a/391/6'}