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  • lfunc_lfunctions • Show schema
    {'Lhash': '770553324393334721269654015040,781675554449286670569588066332,1122261940741667013356097153989', 'a10': 0, 'a2': -2, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 8, 'a8': 2, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 172768.2590114603, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[3, [1]], [5, [1]], [31, [1, -3, 3, -1]]], 'bad_primes': [3, 5, 31], 'central_character': '6975.1', 'coefficient_field': '1.1.1.1', 'conductor': 339338109375, 'conductor_radical': 465, 'degree': 6, 'euler_factors': [[1, 2, 4, 6, 8, 8, 8], [1], [1], [1, -8, 37, -116, 259, -392, 343], [1, 3, 32, 65, 352, 363, 1331], [1, -4, 23, -114, 299, -676, 2197], [1, 7, 44, 179, 748, 2023, 4913], [1, -9, 84, -369, 1596, -3249, 6859], [1, 9, 92, 431, 2116, 4761, 12167], [1, 9, 80, 509, 2320, 7569, 24389], [1, -3, 3, -1], [1, -8, 119, -594, 4403, -10952, 50653], [1, 2, 65, 298, 2665, 3362, 68921], [1, -4, 49, -280, 2107, -7396, 79507], [1, -20, 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-2.030439210375922, -1.6519119692903061, -1.2245010823959737, -0.7875018913932929, -0.3874360044894377, -0.07511494740239666, 0.09843560376026977, 0.0859796241402342, -0.15614249169886968], 'positive_zeros': ['0.60785939300198598557888226678467', '0.61663328547200058508501289005892', '0.885308570468560949032924052227519', '1.38309922256865639846575437420330', '1.77606513184899388648728545548387', '2.07173092937544760936207927847470', '2.28735092345474814453979899205041', '2.38827376021713431231899321574781', '2.85678209184448213077647367074474', '3.37926872636505339908936220494545', '3.77265112442117644263332286865491', '3.80933434500313418211593239467493', '4.24031518038589890799523540922357', '4.36300199068358067643432436278089', '4.49651785315267412896143355890542', '5.03956304990157021347591470711519', '5.09799785104529587554297385863336', '5.41169259019449137488827309704301', '5.50449785074213186716315092871050', '5.78524899841209906941447868611689', '6.04199944283146971207984025718126', '6.24772604838185152067566077583197', '6.78385775431751086821191809665113', '6.82682696850298276513664953129576', '7.33050542589917312070267887838293', '7.51120280184436134082342465306373', '7.60348690792695699046130886392471', '7.77212907183024969976223871218517', '8.053216352951155173599644335041567', '8.150069351271198890982107290516952'], 'prelabel': '6-6975e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.4629521913143115, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e3-0', 'trace_hash': 1321192989185260340, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.60785939300198598557888226678', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '0.61663328547200058508501289006', 'prec': 97}, 'z3': {'__RealLiteral__': 0, 'data': '0.885308570468560949032924052228', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 172768.2590114603, 'bad_primes': [3, 5, 31], 'central_character': '1.1', 'conductor': 339338109375, 'conductor_radical': 465, 'degree': 6, 'dirichlet_coefficients': [1, -2, 0, 0, 0, 0, 8, 2, 0, 0, -3, 0, 4, -16, 0, 0, -7, 0, 9, 0, 0, 6, -9, 0, 0, -8, 0, 0, -9, 0, 3, 0, 0, 14, 0, 0, 8, -18, 0, 0, -2, 0, 4, 0, 0, 18, 20, 0, 27, 0, 0, 0, 25, 0, 0, 16, 0, 18, -2, 0, 2, -6, 0, -4, 0, 0, 15, 0, 0, 0, 12, 0, 2, -16, 0, 0, -24, 0, 12, 0, 0, 4, -13, 0, 0, -8, 0, -6, 15, 0, 32, 0, 0, -40, 0, 0, 7, -54, 0, 0], 'euler11': [1, 3, 32, 65, 352, 363, 1331], 'euler13': [1, -4, 23, -114, 299, -676, 2197], 'euler17': [1, 7, 44, 179, 748, 2023, 4913], 'euler19': [1, -9, 84, -369, 1596, -3249, 6859], 'euler2': [1, 2, 4, 6, 8, 8, 8], 'euler23': [1, 9, 92, 431, 2116, 4761, 12167], 'euler29': [1, 9, 80, 509, 2320, 7569, 24389], 'euler3': [1, 0, 0, 0, 0, 0, 0], 'euler31': [1, -3, 3, -1, 0, 0, 0], 'euler37': [1, -8, 119, -594, 4403, -10952, 50653], 'euler41': [1, 2, 65, 298, 2665, 3362, 68921], 'euler43': [1, -4, 49, -280, 2107, -7396, 79507], 'euler47': [1, -20, 261, -2088, 12267, -44180, 103823], 'euler5': [1, 0, 0, 0, 0, 0, 0], 'euler53': [1, -25, 288, -2301, 15264, -70225, 148877], 'euler59': [1, 2, 103, 162, 6077, 6962, 205379], 'euler61': [1, -2, 131, -204, 7991, -7442, 226981], 'euler67': [1, -15, 236, -2011, 15812, -67335, 300763], 'euler7': [1, -8, 37, -116, 259, -392, 343], 'euler71': [1, -12, 101, -520, 7171, -60492, 357911], 'euler73': [1, -2, 71, -588, 5183, -10658, 389017], 'euler79': [1, -12, 165, -1982, 13035, -74892, 493039], 'euler83': [1, 13, 192, 1287, 15936, 89557, 571787], 'euler89': [1, -15, 338, -2773, 30082, -118815, 704969], 'euler97': [1, -7, 262, -1255, 25414, -65863, 912673], 'euler_factors': [[1, 2, 4, 6, 8, 8, 8], [1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, -8, 37, -116, 259, -392, 343], [1, 3, 32, 65, 352, 363, 1331], [1, -4, 23, -114, 299, -676, 2197], [1, 7, 44, 179, 748, 2023, 4913], [1, -9, 84, -369, 1596, -3249, 6859], [1, 9, 92, 431, 2116, 4761, 12167], [1, 9, 80, 509, 2320, 7569, 24389], [1, -3, 3, -1, 0, 0, 0], [1, -8, 119, -594, 4403, -10952, 50653], [1, 2, 65, 298, 2665, 3362, 68921], [1, -4, 49, -280, 2107, -7396, 79507], [1, -20, 261, -2088, 12267, -44180, 103823], [1, -25, 288, -2301, 15264, -70225, 148877], [1, 2, 103, 162, 6077, 6962, 205379], [1, -2, 131, -204, 7991, -7442, 226981], [1, -15, 236, -2011, 15812, -67335, 300763], [1, -12, 101, -520, 7171, -60492, 357911], [1, -2, 71, -588, 5183, -10658, 389017], [1, -12, 165, -1982, 13035, -74892, 493039], [1, 13, 192, 1287, 15936, 89557, 571787], [1, -15, 338, -2773, 30082, -118815, 704969], [1, -7, 262, -1255, 25414, -65863, 912673]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6975/2/a/ba'], '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': '6-6975e3-1.1-c1e3-0-3', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '6-6975e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.4629521913143115, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 1321192989185260340, 'z1': {'__RealLiteral__': 0, 'data': '0.60785939300198598557888226678', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '770553324393334721269654015040,781675554449286670569588066332,1122261940741667013356097153989', 'Lhash_array': ['770553324393334721269654015040', '781675554449286670569588066332', '1122261940741667013356097153989'], 'factors': ['2-6975-1.1-c1-0-50', '2-6975-1.1-c1-0-51', '2-6975-1.1-c1-0-100'], 'label': '6-6975e3-1.1-c1e3-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6975/2/a/ba'}