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lfunc_lfunctions • Show schema
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{'Lhash': '445584422390141096320872634153,2184521129352206316670064902388', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 4, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 235.04806021792132, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, 1]], [5, [1, -4, 5]]], 'bad_primes': [2, 3, 5], 'central_character': '1920.1', 'coefficient_field': '1.1.1.1', 'conductor': 3686400, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1, 0, 1], [1, -4, 5], [1, 0, -14, 0, 49], [1, 8, 38, 88, 121], [1, 0, -22, 0, 169], [1, 0, -30, 0, 289], [1, 4, 42, 76, 361], [1, 0, -10, 0, 529], [1, 16, 122, 464, 841], [1, 16, 126, 496, 961], [1, 0, -38, 0, 1369], [1, -4, 86, -164, 1681], [1, 0, -70, 0, 1849], [1, 0, -58, 0, 2209], [1, 0, -6, 0, 2809], [1, 16, 182, 944, 3481], [1, 4, 126, 244, 3721], [1, 0, -118, 0, 4489], [1, 0, 142, 0, 5041], [1, 0, -130, 0, 5329], [1, -8, 174, -632, 6241], [1, 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'3.59186126927450692082630023322034', '3.88139454146333423112605202533297', '4.79827108617241633835113521423465', '5.08357540143802882808594765374572', '5.57266325411591586432489183209577', '5.64919098886394390211348230395986', '6.03147878112757713616114365811388', '6.51055679108995187652944943164938', '7.27504118500016891300848084387311', '7.34521936081550446993270867312138', '7.85962669103444162935207870952370', '8.084537019312408245267859670247976', '8.954815229301843090700882632647595', '9.026489002356024184429375589689872', '9.498426309066702463599999221162510'], 'prelabel': '4-1920e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.9155174866275138, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1100257561627148465, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.35150413079906838597716308941', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 235.04806021792132, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 3686400, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 4, 0, 0, 0, -1, 0, -8, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 11, 0, 0, 0, -16, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, 0, 0, 14, 0, 0, 0, 0, 0, -32, 0, 0, 0, -16, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 1, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, -16, 0, 0, 0, 8, 0], 'euler11': [1, 8, 38, 88, 121], 'euler13': [1, 0, -22, 0, 169], 'euler17': [1, 0, -30, 0, 289], 'euler19': [1, 4, 42, 76, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -10, 0, 529], 'euler29': [1, 16, 122, 464, 841], 'euler3': [1, 0, 1, 0, 0], 'euler31': [1, 16, 126, 496, 961], 'euler37': [1, 0, -38, 0, 1369], 'euler41': [1, -4, 86, -164, 1681], 'euler43': [1, 0, -70, 0, 1849], 'euler47': [1, 0, -58, 0, 2209], 'euler5': [1, -4, 5, 0, 0], 'euler53': [1, 0, -6, 0, 2809], 'euler59': [1, 16, 182, 944, 3481], 'euler61': [1, 4, 126, 244, 3721], 'euler67': [1, 0, -118, 0, 4489], 'euler7': [1, 0, -14, 0, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 0, -130, 0, 5329], 'euler79': [1, -8, 174, -632, 6241], 'euler83': [1, 0, 90, 0, 6889], 'euler89': [1, -36, 502, -3204, 7921], 'euler97': [1, 0, 62, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 1, 0, 0], [1, -4, 5, 0, 0], [1, 0, -14, 0, 49], [1, 8, 38, 88, 121], [1, 0, -22, 0, 169], [1, 0, -30, 0, 289], [1, 4, 42, 76, 361], [1, 0, -10, 0, 529], [1, 16, 122, 464, 841], [1, 16, 126, 496, 961], [1, 0, -38, 0, 1369], [1, -4, 86, -164, 1681], [1, 0, -70, 0, 1849], [1, 0, -58, 0, 2209], [1, 0, -6, 0, 2809], [1, 16, 182, 944, 3481], [1, 4, 126, 244, 3721], [1, 0, -118, 0, 4489], [1, 0, 142, 0, 5041], [1, 0, -130, 0, 5329], [1, -8, 174, -632, 6241], [1, 0, 90, 0, 6889], [1, -36, 502, -3204, 7921], [1, 0, 62, 0, 9409]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1920/2/f/i'], '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': '4-1920e2-1.1-c1e2-0-4', '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': '4-1920e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.9155174866275138, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1100257561627148465, 'z1': {'__RealLiteral__': 0, 'data': '0.35150413079906838597716308941', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '445584422390141096320872634153,2184521129352206316670064902388', 'Lhash_array': ['445584422390141096320872634153', '2184521129352206316670064902388'], 'label': '4-1920e2-1.1-c1e2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1920/2/f/i'}