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lfunc_lfunctions • Show schema
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{'Lhash': '1044566241894514070821346207161', 'a10': [0.0, 0.0], 'a2': [6.557366897531871, 0.0], 'a3': [-14.985051383118789, 0.0], 'a4': [10.99906062884676, 0.0], 'a5': [0.0, 0.0], 'a6': [-98.26247989747732, 0.0], 'a7': [156.61533719792632, 0.0], 'a8': [-137.71086464947405, 0.0], 'a9': [-18.448235045289696, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 44.10555044856968, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [121.0, 0]]]], 'bad_primes': [5, 11], 'central_character': '275.1', 'coefficient_field': 'CDF', 'conductor': 275, 'conductor_radical': 55, 'degree': 2, 'euler_factors': [[[1.0, 0], [-6.557366897531871, 0], [32.0, 0]], [[1.0, 0], [14.985051383118789, 0], [243.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-156.61533719792632, 0], [16807.0, 0]], [[1.0, 0], [121.0, 0]], [[1.0, 0], [-895.8282423756755, 0], [371293.0, 0]], [[1.0, 0], [1365.3960973899125, 0], [1419857.0, 0]], [[1.0, 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['0.824017471144216755436612196807528', '2.57243159165048284674086588362462', '4.20109851118775083969194636299037', '4.82532021247059308939357290403461', '5.89070781100477951055503840681134', '6.48667069244365192108348024132304', '8.172105437410844515314736206618746', '8.953931050103450867002357894473480', '10.77585440753687359758707868741459', '11.12252064552110802018345245365731'], 'prelabel': '2-275-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.641200979383901, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.824017471144216755436612196808', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.57243159165048284674086588362', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.20109851118775083969194636299', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 44.10555044856968, 'bad_primes': [5, 11], 'central_character': '1.1', 'conductor': 275, 'conductor_radical': 55, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/275/6/a/l/1/11'], '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': '2-275-1.1-c5-0-25', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-275-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.641200979383901, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.824017471144216755436612196808', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1044566241894514070821346207161', 'Lhash_array': ['1044566241894514070821346207161'], 'label': '2-275-1.1-c5-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/275/6/a/l/1/11'}