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lfunc_lfunctions • Show schema
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{'Lhash': '1661436518581598868933758890948,2372116645183821269955574680626', 'a10': -99, 'a2': 3, 'a3': 0, 'a4': 5, 'a5': -33, 'a6': 0, 'a7': 0, 'a8': 99, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5002.628862019118, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '441.1', 'coefficient_field': '1.1.1.1', 'conductor': 194481, 'conductor_radical': 21, 'degree': 4, 'euler_factors': [[1, -3, 4, -96, 1024], [1], [1, 33, 3472, 103125, 9765625], [1], [1, -1137, 645232, -183114987, 25937424601], [1, 925, 951450, 343446025, 137858491849], [1, 324, 1502434, 460033668, 2015993900449], [1, 2311, 6241998, 5722264789, 6131066257801], [1, 1596, 7604206, 10272403428, 41426511213649], [1, -2217, 42125014, -45473217333, 420707233300201], [1, 4294, 25151367, 122933574394, 819628286980801], [1, 19109, 184470078, 1325093674313, 4808584372417849], [1, 12858, 228491122, 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'primitive': False, 'rational': True, 'root_analytic_conductor': 8.410069235001842, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c5e2-0', 'trace_hash': 574227715659259385, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.31064231601552648464275750368', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.87127008400953892077469303103', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.24669176330310343385865794890', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 5002.628862019118, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 194481, 'conductor_radical': 21, 'degree': 4, 'dirichlet_coefficients': [1, 3, 0, 5, -33, 0, 0, 99, 0, -99, 1137, 0, -925, 0, 0, -459, -324, 0, -2311, -165, 0, 3411, -1596, 0, -2383, -2775, 0, 0, 2217, 0, -4294, -4365, 0, -972, 0, 0, -19109, -6933, 0, -3267, -12858, 0, -2771, 5685, 0, -4788, -23160, 0, 0, -7149, 0, -4625, 31653, 0, -37521, 0, 0, 6651, 41097, 0, -42052, -12882, 0, -6875, 30525, 0, 30763, -1620, 0, 0, -102096, 0, 28577, -57327, 0, -11555, 0, 0, -18464, 15147, 0, -38574, 61179, 0, 10692, -8313, 0, 112563, 29322, 0, 0, -7980, 0, -69480, 76263, 0, 9791, 0, 0, -11915], 'euler11': [1, -1137, 645232, -183114987, 25937424601], 'euler13': [1, 925, 951450, 343446025, 137858491849], 'euler17': [1, 324, 1502434, 460033668, 2015993900449], 'euler19': [1, 2311, 6241998, 5722264789, 6131066257801], 'euler2': [1, -3, 4, -96, 1024], 'euler23': [1, 1596, 7604206, 10272403428, 41426511213649], 'euler29': [1, -2217, 42125014, -45473217333, 420707233300201], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 4294, 25151367, 122933574394, 819628286980801], 'euler37': [1, 19109, 184470078, 1325093674313, 4808584372417849], 'euler41': [1, 12858, 228491122, 1489679032458, 13422659310152401], 'euler43': [1, 2771, 36114396, 407360395553, 21611482313284249], 'euler47': [1, 23160, 570076618, 5311630362120, 52599132235830049], 'euler5': [1, 33, 3472, 103125, 9765625], 'euler53': [1, -31653, 896010526, -13237141939929, 174887470365513049], 'euler59': [1, -41097, 896994610, -29381243916003, 511116753300641401], 'euler61': [1, 42052, 1728407262, 35516963649652, 713342911662882601], 'euler67': [1, -30763, 1698033324, -41533898666641, 1822837804551761449], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 102096, 6091648810, 184204599819696, 3255243551009881201], 'euler73': [1, -28577, 2636499108, -59242166913161, 4297625829703557649], 'euler79': [1, 18464, 3332046261, 56814769351136, 9468276082626847201], 'euler83': [1, -61179, 8589312784, -240986567498097, 15516041187205853449], 'euler89': [1, -29322, 11382011794, -163735791163578, 31181719929966183601], 'euler97': [1, -9791, 17134261944, -84078648456287, 73742412689492826049], 'euler_factors': [[1, -3, 4, -96, 1024], [1, 0, 0, 0, 0], [1, 33, 3472, 103125, 9765625], [1, 0, 0, 0, 0], [1, -1137, 645232, -183114987, 25937424601], [1, 925, 951450, 343446025, 137858491849], [1, 324, 1502434, 460033668, 2015993900449], [1, 2311, 6241998, 5722264789, 6131066257801], [1, 1596, 7604206, 10272403428, 41426511213649], [1, -2217, 42125014, -45473217333, 420707233300201], [1, 4294, 25151367, 122933574394, 819628286980801], [1, 19109, 184470078, 1325093674313, 4808584372417849], [1, 12858, 228491122, 1489679032458, 13422659310152401], [1, 2771, 36114396, 407360395553, 21611482313284249], [1, 23160, 570076618, 5311630362120, 52599132235830049], [1, -31653, 896010526, -13237141939929, 174887470365513049], [1, -41097, 896994610, -29381243916003, 511116753300641401], [1, 42052, 1728407262, 35516963649652, 713342911662882601], [1, -30763, 1698033324, -41533898666641, 1822837804551761449], [1, 102096, 6091648810, 184204599819696, 3255243551009881201], [1, -28577, 2636499108, -59242166913161, 4297625829703557649], [1, 18464, 3332046261, 56814769351136, 9468276082626847201], [1, -61179, 8589312784, -240986567498097, 15516041187205853449], [1, -29322, 11382011794, -163735791163578, 31181719929966183601], [1, -9791, 17134261944, -84078648456287, 73742412689492826049]], 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/6/a/s'], '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': '4-21e4-1.1-c5e2-0-9', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5, 5], 'order_of_vanishing': 2, 'prelabel': '4-21e4-1.1-c5e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.410069235001842, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5e2-0', 'trace_hash': 574227715659259385, 'z1': {'__RealLiteral__': 0, 'data': '1.31064231601552648464275750368', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1661436518581598868933758890948,2372116645183821269955574680626', 'Lhash_array': ['1661436518581598868933758890948', '2372116645183821269955574680626'], 'label': '4-21e4-1.1-c5e2-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/6/a/s'}