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lfunc_lfunctions • Show schema
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{'Lhash': '1013369371541926615480218410373,1468394765138698284710238125612', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 327.9746780876706, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, -2, 1]]], 'bad_primes': [2, 3, 7], 'central_character': '2268.1', 'coefficient_field': '1.1.1.1', 'conductor': 5143824, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1], [1], [1, 0, 7, 0, 25], [1, -2, 1], [1, 0, 10, 0, 121], [1, -10, 51, -130, 169], [1, 0, 31, 0, 289], [1, -4, 42, -76, 361], [1, 0, 34, 0, 529], [1, 0, 55, 0, 841], [1, -4, 66, -124, 961], [1, 14, 123, 518, 1369], [1, 0, 34, 0, 1681], [1, -16, 150, -688, 1849], [1, 0, -14, 0, 2209], [1, 0, -86, 0, 2809], [1, 0, 10, 0, 3481], [1, 2, 123, 122, 3721], [1, -4, 138, -268, 4489], [1, 0, 142, 0, 5041], [1, -22, 267, -1606, 5329], [1, -28, 354, -2212, 6241], [1, 0, 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'6.81137645569507189023563203258392', '7.53231763980010663747111648372583', '7.59942029419832757322927791744694', '8.238281701572889519417981810852576', '8.338441837433368339445617442390249', '8.816874804479432557322232197721219', '9.072816093438087714260956216901650'], 'prelabel': '4-2268e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.255592929125905, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 884868568525673244, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.799407479757812069684742056716', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.15835922364910855749890096371', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.96091800486394431434211509337', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 327.9746780876706, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 5143824, 'conductor_radical': 42, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 22, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 4, 0, 0, 0], 'euler11': [1, 0, 10, 0, 121], 'euler13': [1, -10, 51, -130, 169], 'euler17': [1, 0, 31, 0, 289], 'euler19': [1, -4, 42, -76, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 34, 0, 529], 'euler29': [1, 0, 55, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -4, 66, -124, 961], 'euler37': [1, 14, 123, 518, 1369], 'euler41': [1, 0, 34, 0, 1681], 'euler43': [1, -16, 150, -688, 1849], 'euler47': [1, 0, -14, 0, 2209], 'euler5': [1, 0, 7, 0, 25], 'euler53': [1, 0, -86, 0, 2809], 'euler59': [1, 0, 10, 0, 3481], 'euler61': [1, 2, 123, 122, 3721], 'euler67': [1, -4, 138, -268, 4489], 'euler7': [1, -2, 1, 0, 0], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, -22, 267, -1606, 5329], 'euler79': [1, -28, 354, -2212, 6241], 'euler83': [1, 0, 154, 0, 6889], 'euler89': [1, 0, 175, 0, 7921], 'euler97': [1, -4, 198, -388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, 7, 0, 25], [1, -2, 1, 0, 0], [1, 0, 10, 0, 121], [1, -10, 51, -130, 169], [1, 0, 31, 0, 289], [1, -4, 42, -76, 361], [1, 0, 34, 0, 529], [1, 0, 55, 0, 841], [1, -4, 66, -124, 961], [1, 14, 123, 518, 1369], [1, 0, 34, 0, 1681], [1, -16, 150, -688, 1849], [1, 0, -14, 0, 2209], [1, 0, -86, 0, 2809], [1, 0, 10, 0, 3481], [1, 2, 123, 122, 3721], [1, -4, 138, -268, 4489], [1, 0, 142, 0, 5041], [1, -22, 267, -1606, 5329], [1, -28, 354, -2212, 6241], [1, 0, 154, 0, 6889], [1, 0, 175, 0, 7921], [1, -4, 198, -388, 9409]], 'index': 35, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2268/2/a/f'], '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': '4-2268e2-1.1-c1e2-0-35', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-2268e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.255592929125905, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 884868568525673244, 'z1': {'__RealLiteral__': 0, 'data': '0.799407479757812069684742056716', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1013369371541926615480218410373,1468394765138698284710238125612', 'Lhash_array': ['1013369371541926615480218410373', '1468394765138698284710238125612'], 'label': '4-2268e2-1.1-c1e2-0-35', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2268/2/a/f'}