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lfunc_lfunctions • Show schema
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{'Lhash': '2834088735116929947804893927497', 'a10': 8704, 'a2': 16, 'a3': 170, 'a4': 256, 'a5': 544, 'a6': 2720, 'a7': -2401, 'a8': 4096, 'a9': 9217, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.210501706294226, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -16]], [7, [1, 2401]]], 'bad_primes': [2, 7], 'central_character': '14.1', 'coefficient_field': '1.1.1.1', 'conductor': 14, 'conductor_radical': 14, 'degree': 2, 'euler_factors': [[1, -16], [1, -170, 19683], [1, -544, 1953125], [1, 2401], [1, -48824, 2357947691], [1, 15876, 10604499373], [1, 21418, 118587876497], [1, 716410, 322687697779], [1, 2470000, 1801152661463], [1, -5556826, 14507145975869], [1, -5799348, 26439622160671], [1, 3894430, 129961739795077], [1, 6360858, 327381934393961], [1, 18701296, 502592611936843], [1, -56539068, 1119130473102767], [1, 59894682, 3299763591802133], [1, -165629662, 8662995818654939], [1, -51419016, 11694146092834141], [1, 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[[[1, -165629662, 8662995818654939], 1]], [[[1, -51419016, 11694146092834141], 1]], [[[1, -93546508, 27206534396294947], 1]], [[[1, 95633536, 45848500718449031], 1]], [[[1, -306496402, 58871586708267913], 1]], [[[1, -496474152, 119851595982618319], 1]], [[[1, 371486962, 186940255267540403], 1]], [[[1, 165482550, 350356403707485209], 1]], [[[1, -758016742, 760231058654565217], 1]], [[[1, 904211936, 1093685272684360901], 1]], [[[1, -1981567796, 1304773183829244583], 1]], [[[1, -416378892, 1838459212420154507], 1]], [[[1, 1269209054, 2171893279442309389], 1]], [[[1, 2835276218, 3004041937984268273], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-14-1.1-c9-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/14/10/a/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 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'trace_hash': 153877743173548182, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.23570180506101370749220624969', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.93232421548929015444637441295', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.37302806691458720870578257616', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.210501706294226, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 14, 'conductor_radical': 14, 'degree': 2, 'dirichlet_coefficients': [1, 16, 170, 256, 544, 2720, -2401, 4096, 9217, 8704, 48824, 43520, -15876, -38416, 92480, 65536, -21418, 147472, -716410, 139264, -408170, 781184, -2470000, 696320, -1657189, -254016, -1779220, -614656, 5556826, 1479680, 5799348, 1048576, 8300080, -342688, -1306144, 2359552, -3894430, -11462560, -2698920, 2228224, -6360858, -6530720, -18701296, 12498944, 5014048, -39520000, 56539068, 11141120, 5764801, -26515024, -3641060, -4064256, -59894682, -28467520, 26560256, -9834496, -121789700, 88909216, 165629662, 23674880, 51419016, 92789568, -22130017, 16777216, -8636544, 132801280, 93546508, -5483008, -419900000, -20898304, -95633536, 37752832, 306496402, -62310880, -281722130, -183400960, -117226424, -43182720, 496474152, 35651584, -483885611, -101773728, -371486962, -104491520, -11651392, -299220736, 944660420, 199983104, -165482550, 80224768, 38118276, -632320000, 985889160, 904625088, -389727040, 178257920, 758016742, 92236816, 450010808, -424240384], 'euler11': [1, -48824, 2357947691], 'euler13': [1, 15876, 10604499373], 'euler17': [1, 21418, 118587876497], 'euler19': [1, 716410, 322687697779], 'euler2': [1, -16, 0], 'euler23': [1, 2470000, 1801152661463], 'euler29': [1, -5556826, 14507145975869], 'euler3': [1, -170, 19683], 'euler31': [1, -5799348, 26439622160671], 'euler37': [1, 3894430, 129961739795077], 'euler41': [1, 6360858, 327381934393961], 'euler43': [1, 18701296, 502592611936843], 'euler47': [1, -56539068, 1119130473102767], 'euler5': [1, -544, 1953125], 'euler53': [1, 59894682, 3299763591802133], 'euler59': [1, -165629662, 8662995818654939], 'euler61': [1, -51419016, 11694146092834141], 'euler67': [1, -93546508, 27206534396294947], 'euler7': [1, 2401, 0], 'euler71': [1, 95633536, 45848500718449031], 'euler73': [1, -306496402, 58871586708267913], 'euler79': [1, -496474152, 119851595982618319], 'euler83': [1, 371486962, 186940255267540403], 'euler89': [1, 165482550, 350356403707485209], 'euler97': [1, -758016742, 760231058654565217], 'euler_factors': [[1, -16, 0], [1, -170, 19683], [1, -544, 1953125], [1, 2401, 0], [1, -48824, 2357947691], [1, 15876, 10604499373], [1, 21418, 118587876497], [1, 716410, 322687697779], [1, 2470000, 1801152661463], [1, -5556826, 14507145975869], [1, -5799348, 26439622160671], [1, 3894430, 129961739795077], [1, 6360858, 327381934393961], [1, 18701296, 502592611936843], [1, -56539068, 1119130473102767], [1, 59894682, 3299763591802133], [1, -165629662, 8662995818654939], [1, -51419016, 11694146092834141], [1, -93546508, 27206534396294947], [1, 95633536, 45848500718449031], [1, -306496402, 58871586708267913], [1, -496474152, 119851595982618319], [1, 371486962, 186940255267540403], [1, 165482550, 350356403707485209], [1, -758016742, 760231058654565217]], 'index': 2, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/14/10/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/14/10/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': '2-14-1.1-c9-0-2', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'prelabel': '2-14-1.1-c9-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.685237737388298, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c9-0', 'trace_hash': 153877743173548182, 'z1': {'__RealLiteral__': 0, 'data': '2.23570180506101370749220624969', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10368102
{'Lhash': '2834088735116929947804893927497', 'Lhash_array': ['2834088735116929947804893927497'], 'factors': ['2-14-1.1-c9-0-2'], 'label': '2-14-1.1-c9-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/14/10/a/b'}
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id: 24550984
{'Lhash': '2834088735116929947804893927497', 'Lhash_array': ['2834088735116929947804893927497'], 'factors': ['2-14-1.1-c9-0-2'], 'label': '2-14-1.1-c9-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/14/10/a/b/1/1'}