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lfunc_lfunctions • Show schema
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{'Lhash': '2592848143781852029921733603861', 'a10': [6.343823140858609e-61, 3.5075436819039085], 'a2': [-0.8660254037844386, -0.5], 'a3': [-1.388926261519809, 1.0348351753108351], 'a4': [0.5, 0.8660254037844386], 'a5': [-1.7537718409519543, -3.037621933412389], 'a6': [1.720263014114921, -0.2017304197890018], 'a7': [1.3734140597794828, -2.2613566327317853], 'a8': [0.0, -1.0], 'a9': [0.8582323198787862, -2.874619502667349], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.359831950361911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8660254037844386, 0.5]]], [3, [[1.0, 0], [1.388926261519809, -1.0348351753108351]]], [7, [[1.0, 0], [-1.3734140597794828, 2.2613566327317853]]], [13, [[1.0, 0], [3.5916742536340256, -0.3160317322397611]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.185', 'coefficient_field': 'CDF', 'conductor': 546, 'conductor_radical': 546, 'conjugate': '93930213087047771596507278850', 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'5.24131342388629173026676562606162', '5.91836792610622789186194867020958', '7.00146345037808265584585240318910', '7.60618801076334934745791442569292', '8.313044753775106097650462097456154', '9.630603404507824102346952044167326', '10.69791181603376762153047907432549', '11.19571612410163450900976962797771'], 'prelabel': '2-546-273.185-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': -0.8504138710665697, 'root_number': '-0.8915960558142495 - 0.4528316168913933*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.425206935533', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.04539653380437196431582213952', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.38927437431671370276743646784', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.24131342388629173026676562606', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.359831950361911, 'bad_primes': [2, 3, 7, 13], 'central_character': '273.185', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/u/a/185/5'], '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': '2-546-273.185-c1-0-34', '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': '2-546-273.185-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': -0.42520693553328487, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.04539653380437196431582213952', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2592848143781852029921733603861', 'Lhash_array': ['2592848143781852029921733603861'], 'label': '2-546-273.185-c1-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/u/a/185/5'}