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lfunc_lfunctions • Show schema
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{'Lhash': '2182730913244904411740652198092', 'a10': -31664, 'a2': -16, 'a3': 75, 'a4': 256, 'a5': 1979, 'a6': -1200, 'a7': 10115, 'a8': -4096, 'a9': -14058, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 174.08211262338918, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 16]], [13, [1]]], 'bad_primes': [2, 13], 'central_character': '338.1', 'coefficient_field': '1.1.1.1', 'conductor': 338, 'conductor_radical': 26, 'degree': 2, 'euler_factors': [[1, 16], [1, -75, 19683], [1, -1979, 1953125], [1, -10115, 40353607], [1, 18850, 2357947691], [1], [1, 142403, 118587876497], [1, 83302, 322687697779], [1, 536544, 1801152661463], [1, 2600442, 14507145975869], [1, -2214004, 26439622160671], [1, 18099241, 129961739795077], [1, 26812240, 327381934393961], [1, 42253475, 502592611936843], [1, 35914993, 1119130473102767], [1, 66514064, 3299763591802133], [1, -108164002, 8662995818654939], [1, 207449912, 11694146092834141], [1, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 174.08211262338918, 'bad_primes': [2, 13], 'central_character': '1.1', 'conductor': 338, 'conductor_radical': 26, 'degree': 2, 'dirichlet_coefficients': [1, -16, 75, 256, 1979, -1200, 10115, -4096, -14058, -31664, -18850, 19200, 0, -161840, 148425, 65536, -142403, 224928, -83302, 506624, 758625, 301600, -536544, -307200, 1963316, 0, -2530575, 2589440, -2600442, -2374800, 2214004, -1048576, -1413750, 2278448, 20017585, -3598848, -18099241, 1332832, 0, -8105984, -26812240, -12138000, -42253475, -4825600, -27820782, 8584704, -35914993, 4915200, 61959618, -31413056, -10680225, 0, -66514064, 40489200, -37304150, -41431040, -6247650, 41607072, 108164002, 37996800, -207449912, -35424064, -142196670, 16777216, 0, 22620000, -193015514, -36455168, -40240800, -320281360, 201833497, 57581568, 121628110, 289587856, 147248700, -21325312, -190667750, 0, 112871912, 129695744, 86910489, 428995840, -308254212, 194208000, -281815537, 676055600, -195033150, 77209600, 6374870, 445132512, 0, -137355264, 166050300, 574639888, -164854658, -78643200, -871266886, -991353888, 264993300, 502608896], 'euler11': [1, 18850, 2357947691], 'euler13': [1, 0, 0], 'euler17': [1, 142403, 118587876497], 'euler19': [1, 83302, 322687697779], 'euler2': [1, 16, 0], 'euler23': [1, 536544, 1801152661463], 'euler29': [1, 2600442, 14507145975869], 'euler3': [1, -75, 19683], 'euler31': [1, -2214004, 26439622160671], 'euler37': [1, 18099241, 129961739795077], 'euler41': [1, 26812240, 327381934393961], 'euler43': [1, 42253475, 502592611936843], 'euler47': [1, 35914993, 1119130473102767], 'euler5': [1, -1979, 1953125], 'euler53': [1, 66514064, 3299763591802133], 'euler59': [1, -108164002, 8662995818654939], 'euler61': [1, 207449912, 11694146092834141], 'euler67': [1, 193015514, 27206534396294947], 'euler7': [1, -10115, 40353607], 'euler71': [1, -201833497, 45848500718449031], 'euler73': [1, -121628110, 58871586708267913], 'euler79': [1, -112871912, 119851595982618319], 'euler83': [1, 308254212, 186940255267540403], 'euler89': [1, -6374870, 350356403707485209], 'euler97': [1, 871266886, 760231058654565217], 'euler_factors': [[1, 16, 0], [1, -75, 19683], [1, -1979, 1953125], [1, -10115, 40353607], [1, 18850, 2357947691], [1, 0, 0], [1, 142403, 118587876497], [1, 83302, 322687697779], [1, 536544, 1801152661463], [1, 2600442, 14507145975869], [1, -2214004, 26439622160671], [1, 18099241, 129961739795077], [1, 26812240, 327381934393961], [1, 42253475, 502592611936843], [1, 35914993, 1119130473102767], [1, 66514064, 3299763591802133], [1, -108164002, 8662995818654939], [1, 207449912, 11694146092834141], [1, 193015514, 27206534396294947], [1, -201833497, 45848500718449031], [1, -121628110, 58871586708267913], [1, -112871912, 119851595982618319], [1, 308254212, 186940255267540403], [1, -6374870, 350356403707485209], [1, 871266886, 760231058654565217]], 'index': 110, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/338/10/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/338/10/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': '2-338-1.1-c9-0-110', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 1, 'prelabel': '2-338-1.1-c9-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 13.194018062113951, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c9-0', 'trace_hash': 1876205191986972256, 'z1': {'__RealLiteral__': 0, 'data': '1.72187108407626108074847091668', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20929135
{'Lhash': '2182730913244904411740652198092', 'Lhash_array': ['2182730913244904411740652198092'], 'label': '2-338-1.1-c9-0-110', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/338/10/a/b'}
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id: 24594053
{'Lhash': '2182730913244904411740652198092', 'Lhash_array': ['2182730913244904411740652198092'], 'label': '2-338-1.1-c9-0-110', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/338/10/a/b/1/1'}