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lfunc_lfunctions • Show schema
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{'Lhash': '1807078648304580297713259241521,2279829978622165233830338546670', 'a10': 2, 'a2': 2, 'a3': 1, 'a4': 3, 'a5': 1, 'a6': 2, 'a7': -2, 'a8': 4, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.45520039651585, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 1]], [269, [1, 2, 1]]], 'bad_primes': [2, 269], 'central_character': '538.1', 'coefficient_field': '1.1.1.1', 'conductor': 289444, 'conductor_radical': 538, 'degree': 4, 'euler_factors': [[1, -2, 1], [1, -1, 3, -3, 9], [1, -1, 7, -5, 25], [1, 2, 15, 14, 49], [1, -6, 31, -66, 121], [1, -10, 51, -130, 169], [1, 4, 25, 68, 289], [1, -4, 42, -76, 361], [1, -2, -5, -46, 529], [1, -13, 97, -377, 841], [1, 12, 85, 372, 961], [1, 0, 61, 0, 1369], [1, 10, 94, 410, 1681], [1, 10, 59, 430, 1849], [1, 9, 85, 423, 2209], [1, 0, 106, 0, 2809], [1, 5, 43, 295, 3481], [1, 2, 123, 122, 3721], [1, -18, 163, -1206, 4489], [1, 6, 34, 426, 5041], [1, 0, 133, 0, 5329], 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-3.0633147879812945], 'positive_zeros': ['1.42553369830711364388203249635052', '1.79846874068588125902600475990636', '3.01077873099390255308634150018560', '3.37919496802167730530231627105351', '3.62739899889701253609734948046660', '4.20321158622666857924280124018603', '4.94760952852127934613324027834640', '5.51402124410881792477446818017950', '6.11355403001466061285262485648704', '6.45769168146058318023883440280627', '6.59432356543163022882436908892130', '7.08655305238369845374278922641428', '8.129152520931152539430414403721556', '8.370356655563098782338215071682681', '8.801734598099893482141580861157614', '9.215065162740532783467983571224047', '9.776204173864185958574316016086295', '10.12074581127786568131326877849541', '10.95106837881552665093781446547298', '11.14746901950943647195748594239737'], 'prelabel': '4-538e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.0726677564783236, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 375986409058384954, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.42553369830711364388203249635', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.79846874068588125902600475991', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.01077873099390255308634150019', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.45520039651585, 'bad_primes': [2, 269], 'central_character': '1.1', 'conductor': 289444, 'conductor_radical': 538, 'degree': 4, 'dirichlet_coefficients': [1, 2, 1, 3, 1, 2, -2, 4, -2, 2, 6, 3, 10, -4, 1, 5, -4, -4, 4, 3, -2, 12, 2, 4, -6, 20, -2, -6, 13, 2, -12, 6, 6, -8, -2, -6, 0, 8, 10, 4, -10, -4, -10, 18, -2, 4, -9, 5, -11, -12, -4, 30, 0, -4, 6, -8, 4, 26, -5, 3, -2, -24, 4, 7, 10, 12, 18, -12, 2, -4, -6, -8, 0, 0, -6, 12, -12, 20, -9, 5, -2, -20, 10, -6, -4, -20, 13, 24, -11, -4, -20, 6, -12, -18, 4, 6, 2, -22, -12, -18], 'euler11': [1, -6, 31, -66, 121], 'euler13': [1, -10, 51, -130, 169], 'euler17': [1, 4, 25, 68, 289], 'euler19': [1, -4, 42, -76, 361], 'euler2': [1, -2, 1, 0, 0], 'euler23': [1, -2, -5, -46, 529], 'euler29': [1, -13, 97, -377, 841], 'euler3': [1, -1, 3, -3, 9], 'euler31': [1, 12, 85, 372, 961], 'euler37': [1, 0, 61, 0, 1369], 'euler41': [1, 10, 94, 410, 1681], 'euler43': [1, 10, 59, 430, 1849], 'euler47': [1, 9, 85, 423, 2209], 'euler5': [1, -1, 7, -5, 25], 'euler53': [1, 0, 106, 0, 2809], 'euler59': [1, 5, 43, 295, 3481], 'euler61': [1, 2, 123, 122, 3721], 'euler67': [1, -18, 163, -1206, 4489], 'euler7': [1, 2, 15, 14, 49], 'euler71': [1, 6, 34, 426, 5041], 'euler73': [1, 0, 133, 0, 5329], 'euler79': [1, 9, 175, 711, 6241], 'euler83': [1, -10, 178, -830, 6889], 'euler89': [1, 11, 205, 979, 7921], 'euler97': [1, -2, 182, -194, 9409], 'euler_factors': [[1, -2, 1, 0, 0], [1, -1, 3, -3, 9], [1, -1, 7, -5, 25], [1, 2, 15, 14, 49], [1, -6, 31, -66, 121], [1, -10, 51, -130, 169], [1, 4, 25, 68, 289], [1, -4, 42, -76, 361], [1, -2, -5, -46, 529], [1, -13, 97, -377, 841], [1, 12, 85, 372, 961], [1, 0, 61, 0, 1369], [1, 10, 94, 410, 1681], [1, 10, 59, 430, 1849], [1, 9, 85, 423, 2209], [1, 0, 106, 0, 2809], [1, 5, 43, 295, 3481], [1, 2, 123, 122, 3721], [1, -18, 163, -1206, 4489], [1, 6, 34, 426, 5041], [1, 0, 133, 0, 5329], [1, 9, 175, 711, 6241], [1, -10, 178, -830, 6889], [1, 11, 205, 979, 7921], [1, -2, 182, -194, 9409]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/538/2/a/b'], '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': '4-538e2-1.1-c1e2-0-0', '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': '4-538e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.0726677564783236, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 375986409058384954, 'z1': {'__RealLiteral__': 0, 'data': '1.42553369830711364388203249635', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1807078648304580297713259241521,2279829978622165233830338546670', 'Lhash_array': ['1807078648304580297713259241521', '2279829978622165233830338546670'], 'label': '4-538e2-1.1-c1e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/538/2/a/b'}