-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '70000647235660924520973756840', 'a10': [13.67923363368569, -0.3562360658977194], 'a2': [-1.9993221534260388, 0.05206656143694706], 'a3': [0, 0], 'a4': [3.9945781463602654, -0.20819565946721227], 'a5': [-6.841935708182373, 0], 'a6': [0, 0], 'a7': [0, -12.249559041478863], 'a8': [-7.975608549515044, 0.624234142692094], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.63765008224431, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.9993221534260388, -0.05206656143694706]]], [3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [0, -4.358898943540674]]]], 'bad_primes': [2, 3, 19], 'central_character': '684.343', 'coefficient_field': 'CDF', 'conductor': 684, 'conductor_radical': 114, 'conjugate': '1056280025658052047813077045955', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.9993221534260388, -0.05206656143694706]], [[1.0, 0], [0, 0]], [[1.0, 0], [6.841935708182373, 0], [25.0, 0]], [[1.0, 0], [0, 12.249559041478863], [-49.0, 0]], [[1.0, 0], [0, 6.1765490460400585], [-121.0, 0]], [[1.0, 0], [24.757831279236225, 0], [169.0, 0]], [[1.0, 0], [7.41499409138308, 0], [289.0, 0]], [[1.0, 0], [0, -4.358898943540674]], [[1.0, 0], [0, 31.323496693548048], [-529.0, 0]], [[1.0, 0], [-25.149213051636, 0], [841.0, 0]], [[1.0, 0], [0, -47.16008649903359], [-961.0, 0]], [[1.0, 0], [-12.84223501093464, 0], [1369.0, 0]], [[1.0, 0], [-32.875123445768814, 0], [1681.0, 0]], [[1.0, 0], [0, 37.20360740387691], [-1849.0, 0]], [[1.0, 0], [0, 3.787648073330637], [-2209.0, 0]], [[1.0, 0], [10.829043449744177, 0], [2809.0, 0]], [[1.0, 0], [0, -76.16027448696838], [-3481.0, 0]], [[1.0, 0], [37.40149845103027, 0], [3721.0, 0]], [[1.0, 0], [0, 7.640186453403929], [-4489.0, 0]], [[1.0, 0], [0, 30.73846567423135], [-5041.0, 0]], [[1.0, 0], [-108.83190588792978, 0], [5329.0, 0]], [[1.0, 0], [0, -34.7805520652318], [-6241.0, 0]], [[1.0, 0], [0, -100.12521692698212], [-6889.0, 0]], [[1.0, 0], [17.25561554051466, 0], [7921.0, 0]], [[1.0, 0], [97.18919266816772, 0], [9409.0, 0]], [[1.0, 0], [146.88573692914915, 0], [10201.0, 0]], [[1.0, 0], [0, 85.01187066332331], [-10609.0, 0]], [[1.0, 0], [0, -195.4566123579778], [-11449.0, 0]], [[1.0, 0], [18.76071661069064, 0], [11881.0, 0]], [[1.0, 0], [80.54573479353733, 0], [12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-684-4.3-c2-0-4', 'leading_term': '0.081234319277324070026492834951684415696303397064394928', '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/684/3/g/c/343/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.08123431927732407, -0.005217798094359312, -0.10030391571681621, -0.20327967010758388, -0.31335595061779353, -0.42968489394642173, -0.5513455448429627, -0.6773301559946326, -0.8065320841444936, -0.9377361880459163, -1.0696125524420788, -1.2007142569873137, -1.3294797857910112, -1.4542405371232132, -1.5732337476897487, -1.68462099450847, -1.7865122815652503, -1.8769955592250893, -1.9541713626913528, -2.0161920926318744, -2.0613052978318085, -2.0879001584305694, -2.0945562117423004, -2.080093214402819, -2.0436208988955107, -1.9845872642313425, -1.9028239449473818, -1.798587135091188, -1.6725925098784453, -1.5260425923551328, -1.3606450602146967, -1.1786205826534062, -0.9826989214703903, -0.7761022259173819, -0.5625146969632635, -0.34603809187561413, -0.13113288074973306, 0.07745475263277446, 0.27477945983162533, 0.45579578406129095, 0.6154682319489769, 0.7488904197888355, 0.851410918240167, 0.9187630131654483, 0.9471952383319756, 0.9335992335527351, 0.8756312546628962, 0.7718235237098683, 0.6216815715380651, 0.425763801121842, 0.18573969640882443, -0.09557657726050699, -0.41421998791053405, -0.7650981036391166, -1.1420457626848906, -1.5379117094077115, -1.9446770827824014, -2.353604701668976, -2.75541710712719, -3.1405003246205765, -3.4991293291722556, -3.8217102674612753, -4.0990336465764114, -4.322531973684839, -4.484534756957373, -4.578513385916592, -4.599308225329391, -4.543330302194682, -4.408730255414911, -4.195527760282775, -3.9056954347685124, -3.5431922728532568, -3.1139429138515027, -2.6257605187238635, -2.088212648902893, -1.5124312860615734, -0.910869941278218, -0.29701262207194523, 0.3149588055191259, 0.9105306688482325, 1.4752472883693866, 1.9951136237540972, 2.456998926640131, 2.8490289684230716, 3.1609542066491847, 3.384481464597479, 3.513557341176628, 3.5445926432066397, 3.476618624709382, 3.3113676970806503, 3.053273493095613, 2.709387664599059, 2.289213492738418, 1.8044592033654325, 1.26871671244125, 0.6970742748111515, 0.1056740702539761, -0.48877196934621747, -1.0694929053285336, -1.6201795155275143, -2.1254975402337832, -2.571575738071426, -2.946451419850474, -3.240457159783983, -3.4465340527654216, -3.5604591557138496, -3.58097755713226, -3.509832774878935, -3.3516927790153983, -3.1139727475110783, -2.806559546630154, -2.441446735195053, -2.032292469648252, -1.593915884939937, -1.1417502040939669, -0.6912728617670066, -0.2574342106235781, 0.1458931629103478, 0.5064229006102345, 0.8139007954447824, 1.0604700124218966, 1.2409403927502682, 1.3529502725526077, 1.3970134591840213, 1.376448626135502, 1.2971932284971845, 1.1675089058793793, 0.9975900213382418, 0.7990912767130562, 0.5845940501395013, 0.36703404252066546, 0.15911484608334742, -0.027266955236282104, -0.18155965021715734, -0.29503296219493247, -0.3611713833882871, -0.3759657321171404, -0.33808866883057526, -0.24894493448591165, -0.11259263714156395, 0.06446222906583132, 0.27358995425249477, 0.5044662345035787, 0.7455873503090273, 0.9848481069449098, 1.2101558252959137, 1.4100514263501538, 1.5743077179401272, 1.6944754500792392, 1.7643495739881145, 1.7803313716815594, 1.741666603263803, 1.6505453698101946, 1.5120557756054585, 1.3339904113115126, 1.126511850126224, 0.9016904111735744, 0.6729340512971195, 0.45433606196531834, 0.2599709636410904, 0.10317234102029008, -0.004171857279689348, -0.05227095728223316, -0.03399622753701343, 0.054671912089104366, 0.2143395935880917, 0.44205711977291284, 0.731349919168273, 1.0724258836831249, 1.452553369161564, 1.8565954078156597, 2.26767742771829, 2.6679584301276322, 3.039469540847284, 3.364979474278005, 3.6288440026290782, 3.8177961928149275, 3.9216360426453125, 3.933782188819376, 3.851654432255135, 3.6768636824363825, 3.4151952124352363, 3.076381404966439, 2.6736709558541727, 2.2232122406448767, 1.7432786829687996, 1.25337294262752, 0.77325406206152, 0.32193693633024917, -0.08328373651144239, -0.42773273507460546, -0.7001271534319207, -0.8931784488544529, -1.0039871778019969, -1.0342039057164667, -0.9899415009315848, -0.881436901781701, -0.7224738341126231, -0.5295911604665066, -0.3211138551960886, -0.11605433809166951, 0.06705956015147077, 0.21136791116414, 0.30280849958914596, 0.33112902931706556, 0.29072174923668115, 0.18122798906996046, 0.007870615738173166, -0.21851446599537885, -0.4817615515044083, -0.7609705614892108, -1.0313953570536796, -1.2655893678812797, -1.4347580248839868, -1.5102547415623147, -1.4651473724411408, -1.2757758053678407, -0.9232190595134313, -0.39459220514702276, 0.3159003817674912, 1.2062186706526414, 2.266096903572257, 3.4770423077070074, 4.812736059324774, 6.239829690831121, 7.719109667112303, 9.20698328052636, 10.657221385251997, 12.022878793437458, 13.258302236958812, 14.321129326343787, 15.174180355873519, 15.787148301264121, 16.138000854256536, 16.214021485831623, 16.0124337167699, 15.540573159818374, 14.815594450546813, 13.863723735189597, 12.719090688331102, 11.422195837098114, 10.018088077529395, 8.554342616301431, 7.0789402792438, 5.638154560558261, 4.27455258788587, 3.025210298684411, 1.9202308269224533, 0.9816389541797774, 0.22270433128428838, -0.35227689520360306, -0.7477371575365839, -0.9761493935606749, -1.0569399323741895, -1.0150679633178579, -0.8793550701585389, -0.6806614833151522], 'positive_zeros': ['0.05522077394438019461629499665361', '2.14591557301009429407752560972462', '2.96927096440855682193165537863387', '4.54004845834967408226854416996921', '5.63539051450525260206695057013526', '6.83363691690345366388660355158921', '7.72521605868533555764780223792178', '8.183141490619840091949933476665627', '9.430564029929435844971137242752656', '9.579134496293842739597607081547133'], 'prelabel': '2-684-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.317134475811972, 'root_angle': -0.516575173858092, 'root_number': '-0.0520489148668030693564225215771201197644237086399528592 - 0.9986445365900663086773937187854689984063196257544168323*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.258287586929046', 'prec': 60}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.05522077394438019461629499665', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.14591557301009429407752560972', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.96927096440855682193165537863', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 18.63765008224431, 'bad_primes': [2, 3, 19], 'central_character': '4.3', 'conductor': 684, 'conductor_radical': 114, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/684/3/g/c/343/2'], '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': '2-684-4.3-c2-0-4', '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': '2-684-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.317134475811972, 'root_angle': -0.258287586929046, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.05522077394438019461629499665', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '70000647235660924520973756840', 'Lhash_array': ['70000647235660924520973756840'], 'label': '2-684-4.3-c2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/684/3/g/c/343/2'}