-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1060700384235330975514987986778', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-5.527022052227175, 5.527022052227175], 'a6': [0, 0], 'a7': [0, -7.794208764923178], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 31.389726454306206, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1152.737', 'coefficient_field': 'CDF', 'conductor': 1152, 'conductor_radical': 6, 'conjugate': '506575293626106063219751404195', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.527022052227175, -5.527022052227175], [0, -25.0]], [[1.0, 0], [0, 7.794208764923178], [-49.0, 0]], [[1.0, 0], [2.4852139512740288, -2.4852139512740288], [0, -121.0]], [[1.0, 0], [13.32421947580812, -13.32421947580812], [0, -169.0]], [[1.0, 0], [0, -5.86338195977415], [-289.0, 0]], [[1.0, 0], [-18.571231579087886, 18.571231579087886], [0, -361.0]], [[1.0, 0], [34.313611463390316, 0], [529.0, 0]], [[1.0, 0], [-21.48723276890818, -21.48723276890818], [0, 841.0]], [[1.0, 0], [-30.6116666982024, 0], [961.0, 0]], [[1.0, 0], [30.327443928113937, 30.327443928113937], [0, 1369.0]], [[1.0, 0], [3.1270862845332075, 0], [1681.0, 0]], [[1.0, 0], [9.949806526505933, 9.949806526505933], [0, 1849.0]], [[1.0, 0], [0, 38.40521162857856], [-2209.0, 0]], [[1.0, 0], [-61.18258825503558, 61.18258825503558], [0, -2809.0]], [[1.0, 0], [2.988917194987094, -2.988917194987094], [0, -3481.0]], [[1.0, 0], [3.8865910196626596, -3.8865910196626596], [0, -3721.0]], [[1.0, 0], [47.02417572587548, -47.02417572587548], [0, -4489.0]], [[1.0, 0], [-97.54160918701072, 0], [5041.0, 0]], [[1.0, 0], [0, 106.90398254124464], [-5329.0, 0]], [[1.0, 0], [-96.82550355165168, 0], [6241.0, 0]], [[1.0, 0], [-88.8242265602663, -88.8242265602663], [0, 6889.0]], [[1.0, 0], [-54.865145856855996, 0], [7921.0, 0]], [[1.0, 0], [5.001942056516391, 0], [9409.0, 0]], [[1.0, 0], [-37.24806539535399, 37.24806539535399], [0, -10201.0]], [[1.0, 0], [0, 188.02776463369094], [-10609.0, 0]], [[1.0, 0], [-35.22529362936222, 35.22529362936222], [0, -11449.0]], [[1.0, 0], [-93.00730675902268, 93.00730675902268], [0, -11881.0]], [[1.0, 0], [0, 3.808332951543159], [-12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 17, 'label': '2-1152-48.5-c2-0-17', 'leading_term': '0.964314885693465684762717367234327113657247608942585676', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1152/3/j/b/737/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.9643148856934657, 1.0354963492927183, 1.0865455491554008, 1.1169383128127186, 1.1262321178507615, 1.1140763707059664, 1.0802293374912266, 1.0245810368316226, 0.9471810627272228, 0.8482700161335647, 0.728312996484997, 0.5880334431913972, 0.42844552263699515, 0.25088322601686663, 0.05702437351003544, -0.15109219365411297, -0.37105781396984133, -0.6000949943121531, -0.835069350938977, -1.0725133946028529, -1.3086627395972434, -1.5395049688443903, -1.7608410081490737, -1.9683584584449434, -2.157715912893897, -2.324636855531038, -2.46501131104195, -2.575003004111549, -2.6511594058265935, -2.6905217090007407, -2.6907314995829252, -2.650130692879192, -2.5678511956931325, -2.4438907516619026, -2.279171537784562, -2.075578313231276, -1.8359732812421814, -1.5641853113973796, -1.264971778297703, -0.9439519943591462, -0.6075120345380044, -0.2626816498667746, 0.08301507962712588, 0.42173272241820686, 0.7454975000229955, 1.0464157837179964, 1.3168926957114193, 1.5498546902521313, 1.738969405933664, 1.8788556828541372, 1.9652764573922648, 1.995307307684588, 1.9674737419636321, 1.8818509089375757, 1.7401202641216686, 1.5455788379728186, 1.303098099592118, 1.0190309615773057, 0.70106718478035, 0.35803926403810765, -0.00031725320765724793, -0.363643211353437, -0.7212674884159294, -1.0625416718917442, -1.3771872448416322, -1.6556437035891818, -1.8894053413616252, -2.0713341645802394, -2.1959365990615813, -2.2595923152453983, -2.260724660107737, -2.1999038147454546, -2.079875866686703, -1.9055134405483642, -1.6836862960875087, -1.423053287642215, -1.133780176975907, -0.8271908844939809, -0.5153627260626431, -0.21067888592456377, 0.07464630521711976, 0.32905190151517294, 0.5421060869019604, 0.7049540181203077, 0.8107188819338887, 0.8548382978505102, 0.8353199976134538, 0.7529032647927285, 0.6111158553685756, 0.41621994320164624, 0.17704491165606512, -0.09529061382998369, -0.38776040773842985, -0.6859042657665915, -0.9743775806766298, -1.2375570008151022, -1.4601791252689584, -1.6279868595199607, -1.7283567120426298, -1.7508800617320934, -1.6878723311927137, -1.5347860760315366, -1.2905072077617834, -0.9575178171414711, -0.5419142135214723, -0.053274654009604114, 0.4956224276060519, 1.0892223327090798, 1.7097463149425969, 2.3378521612540766, 2.9533777537417345, 3.536137727337841, 4.0667400216164165, 4.527387193990534, 4.902626960928864, 5.180017642654085, 5.350677011697346, 5.409687417085931, 5.35633582784902, 5.19417439307237, 4.930894966434222, 4.578019451758553, 4.150416412676597, 3.665662750107347, 3.1432769768836675, 2.6038573151104427, 2.068163149208833, 1.5561819806529387, 1.086225715303085, 0.6740997233999174, 0.3323855953606003, 0.06987392696225292, -0.1088230358691581, -0.20345721914650305, -0.21811679324357533, -0.16098260493655364, -0.043877782094940185, 0.11837012199168832, 0.3087252123696683, 0.5088596781084134, 0.70014571039149, 0.8646731995146208, 0.9862410475869116, 1.0512700991362465, 1.049588544394354, 0.9750461244530483, 0.8259213593384965, 0.6050959914813573, 0.31998242966583706, -0.017797366765471934, -0.3929700406519442, -0.7873816699639469, -1.180945025869265, -1.5527166972484958, -1.8820494097748675, -2.14975944254169, -2.3392466777961873, -2.437505726734318, -2.4359708041129666, -2.331144446312201, -2.124970474220691, -1.8249243206098695, -1.4438083523937042, -0.999255385490784, -0.5129593978765439, -0.00966764089509609, 0.484017915978112, 0.9409703869390103, 1.3349310541502672, 1.6418927153115002, 1.8413990801947178, 1.9176888345374414, 1.8606197988757556, 1.6663191213755641, 1.33751916900675, 0.8835550387928435, 0.3200175581125655, -0.3319256797670435, -1.0465103181610576, -1.7946083035695302, -2.5451513172938056, -3.266670351641478, -3.9288696152317404, -4.504149799697049, -4.968997306203741, -5.305162326558748, -5.5005594406212, -5.549839105912287, -5.454596312897423, -5.223202794249199, -4.870270391077102, -4.41577428641072, -3.8838845876280046, -3.3015719969331148, -2.6970669955083575, -2.0982612124554856, -1.5311438270249689, -1.0183646212502147, -0.5780086331579575, -0.22265555465951722, 0.04121931705002071, 0.21346573578687905, 0.3000864042143408, 0.3126814150258426, 0.26754199291089353, 0.18444811295463123, 0.08524339559280639, -0.007724694330056985, -0.07320185959167365, -0.09256009967659369, -0.05116843564311094, 0.06048857444528558, 0.2460198932901084, 0.5027206125867811, 0.8215808605769356, 1.1877180528526066, 1.5812128978378315, 1.9783036489368602, 2.3528695212049753, 2.678114483325664, 2.9283481091874974, 3.080751845556849, 3.117017575130301, 3.024750963755939, 2.798544572642981, 2.440644449044163, 1.9611578329873873, 1.3777773335632015, 0.7150267666409722, 0.003063967160843318, -0.7238956033861335, -1.429445574614436, -2.0770368739622467, -2.632085097093355, -3.064008675478854, -3.348071408304186, -3.4669128627989343, -3.411667605252645, -3.1825982317384542, -2.7891963119751066, -2.2497378742955183, -1.5903139269326152, -0.8433895887257162, -0.045975560349509906, 0.7624790753786191, 1.5423450777879169, 2.2560838943851844, 2.8703906819080323, 3.358075983398632, 3.699568120582148, 3.883941698902405, 3.909407307771083, 3.783231679766701, 3.521094074055999, 3.14592110898219, 2.686276290768548, 2.174409798543075], 'positive_zeros': ['0.836745065276158233240050955380912', '2.44680961002433006952159882145594', '3.51557373433193329794559473747465', '4.67163991249912967350646090595825', '5.31216228113475405764850832119075', '6.15829871353521172485223810841722', '7.69558405322020091211822580933634', '7.986027167031818606875499744598890', '8.727558699487891531058668888037191', '9.669095102433463690849118088672204'], 'prelabel': '2-1152-48.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.602653519030621, 'root_angle': 0.24518013782628045, 'root_number': '0.7177323520474645306362307581248910907184259277379314277 + 0.6963190869309949036143177690293894186451991017221830120*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.12259006891314023', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.836745065276158233240050955381', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.44680961002433006952159882146', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.51557373433193329794559473747', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 31.389726454306206, 'bad_primes': [2, 3], 'central_character': '48.5', 'conductor': 1152, 'conductor_radical': 6, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1152/3/j/b/737/2'], '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': '2-1152-48.5-c2-0-17', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-1152-48.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.602653519030621, 'root_angle': 0.12259006891314023, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.836745065276158233240050955381', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1060700384235330975514987986778', 'Lhash_array': ['1060700384235330975514987986778'], 'label': '2-1152-48.5-c2-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1152/3/j/b/737/2'}