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lfunc_lfunctions • Show schema
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{'Lhash': '1368779308191018454063861902133,1487040458613912614861404322504', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 4, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 215.86879141541732, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, -4, 5]], [23, [1, 0, 1]]], 'bad_primes': [2, 5, 23], 'central_character': '1840.1', 'coefficient_field': '1.1.1.1', 'conductor': 3385600, 'conductor_radical': 230, 'degree': 4, 'euler_factors': [[1], [1, 0, -2, 0, 9], [1, -4, 5], [1, 0, -13, 0, 49], [1, 0, 22, 0, 121], [1, 0, -22, 0, 169], [1, 0, -9, 0, 289], [1, -16, 102, -304, 361], [1, 0, 1], [1, -10, 83, -290, 841], [1, -10, 87, -310, 961], [1, 0, -25, 0, 1369], [1, 14, 131, 574, 1681], [1, 0, -70, 0, 1849], [1, 0, -90, 0, 2209], [1, 0, -105, 0, 2809], [1, -6, 127, -354, 3481], [1, 12, 158, 732, 3721], [1, 0, 35, 0, 4489], [1, 26, 311, 1846, 5041], [1, 0, -82, 0, 5329], [1, 28, 354, 2212, 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'5.09448648118850537508863782361339', '5.33328016647002968014205843757266', '5.95137489070646669466531836892196', '6.09269721317024906131007890851651', '6.74325802401862703672458195400883', '7.00935219860697231240192946526001', '7.43975023962131211940246693186669', '7.76313551498356507799038903368652', '8.375765579340527809822076059587757', '8.937412046044829089611044227641398', '8.951532487729763002332319976483236', '9.576148030410108098600644602423851'], 'prelabel': '4-1840e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.833076306560515, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1807802232999185860, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.07977648410735711665803284198', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.17306808228243964742902952309', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.83492881296117993969960863091', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 215.86879141541732, 'bad_primes': [2, 5, 23], 'central_character': '1.1', 'conductor': 3385600, 'conductor_radical': 230, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 11, 0, 0, 0, 10, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 8, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26, 0, 0, 0, 0, 0, 0, 0, -28, 0, -5, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, 0, -22, 0, 169], 'euler17': [1, 0, -9, 0, 289], 'euler19': [1, -16, 102, -304, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 1, 0, 0], 'euler29': [1, -10, 83, -290, 841], 'euler3': [1, 0, -2, 0, 9], 'euler31': [1, -10, 87, -310, 961], 'euler37': [1, 0, -25, 0, 1369], 'euler41': [1, 14, 131, 574, 1681], 'euler43': [1, 0, -70, 0, 1849], 'euler47': [1, 0, -90, 0, 2209], 'euler5': [1, -4, 5, 0, 0], 'euler53': [1, 0, -105, 0, 2809], 'euler59': [1, -6, 127, -354, 3481], 'euler61': [1, 12, 158, 732, 3721], 'euler67': [1, 0, 35, 0, 4489], 'euler7': [1, 0, -13, 0, 49], 'euler71': [1, 26, 311, 1846, 5041], 'euler73': [1, 0, -82, 0, 5329], 'euler79': [1, 28, 354, 2212, 6241], 'euler83': [1, 0, -157, 0, 6889], 'euler89': [1, -28, 374, -2492, 7921], 'euler97': [1, 0, 2, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -2, 0, 9], [1, -4, 5, 0, 0], [1, 0, -13, 0, 49], [1, 0, 22, 0, 121], [1, 0, -22, 0, 169], [1, 0, -9, 0, 289], [1, -16, 102, -304, 361], [1, 0, 1, 0, 0], [1, -10, 83, -290, 841], [1, -10, 87, -310, 961], [1, 0, -25, 0, 1369], [1, 14, 131, 574, 1681], [1, 0, -70, 0, 1849], [1, 0, -90, 0, 2209], [1, 0, -105, 0, 2809], [1, -6, 127, -354, 3481], [1, 12, 158, 732, 3721], [1, 0, 35, 0, 4489], [1, 26, 311, 1846, 5041], [1, 0, -82, 0, 5329], [1, 28, 354, 2212, 6241], [1, 0, -157, 0, 6889], [1, -28, 374, -2492, 7921], [1, 0, 2, 0, 9409]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1840/2/e/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': '4-1840e2-1.1-c1e2-0-5', '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': '4-1840e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.833076306560515, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1807802232999185860, 'z1': {'__RealLiteral__': 0, 'data': '1.07977648410735711665803284198', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1368779308191018454063861902133,1487040458613912614861404322504', 'Lhash_array': ['1368779308191018454063861902133', '1487040458613912614861404322504'], 'label': '4-1840e2-1.1-c1e2-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1840/2/e/b'}