-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '270451862151777400142089614878', 'a10': [-1.667283097158264, 1.9241472662654515], 'a2': [-1.8569709758218576, 1.1934027818949042], 'a3': [-0.9898214418809327, -0.14231483827328514], 'a4': [1.1933009792065123, -2.6129646661787627], 'a5': [1.1066848909665914, -0.324952003322399], 'a6': [2.0079086127192953, -0.9169811382176583], 'a7': [-2.2374425700484997, -1.412037798975213], 'a8': [0.27410655442146536, 1.906452961745731], 'a9': [0.9594929736144974, 0.28173255684142967], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.9898214418809327, 0.14231483827328514]]], [7, [[1.0, 0], [2.2374425700484997, 1.412037798975213]]], [23, [[1.0, 0], [-0.10839130767961243, -4.79460648274908]]]], 'bad_primes': [3, 7, 23], 'central_character': '483.34', 'coefficient_field': 'CDF', 'conductor': 483, 'conductor_radical': 483, 'conjugate': '1800246653951776296498615450965', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.8569709758218576, -1.1934027818949042], [0.8308300260037729, -1.8192639907090367]], [[1.0, 0], [0.9898214418809327, 0.14231483827328514]], [[1.0, 0], [-1.1066848909665914, 0.324952003322399], [4.206267664155906, -2.703204087277988]], [[1.0, 0], [2.2374425700484997, 1.412037798975213]], [[1.0, 0], [0.09831164268458638, -0.1529759020343253], [-4.569565143020751, -10.005951948899702]], [[1.0, 0], [3.1170165257169784, 2.7009101943520024], [1.850092897552707, 12.867678744452126]], [[1.0, 0], [-2.2451903708456555, -4.916281147917518], [-11.132632477069846, 12.84774276402239]], [[1.0, 0], [-0.21457149536838085, 0.4698460367807091], [-12.442353944960416, -14.359241912730907]], [[1.0, 0], [-0.10839130767961243, -4.79460648274908]], [[1.0, 0], [-3.4727397700063047, -7.604239393060841], [-18.990961284413267, 21.91673765627349]], [[1.0, 0], [3.4817041034910345, -0.500593476195239], [29.744282182049417, -8.73370926208432]], [[1.0, 0], [0.13913272607735466, -0.47384254971352036], [-31.126380714753704, -20.00371024585711]], [[1.0, 0], [2.659525065770548, 9.05751057800085], [-34.49139484607843, 22.1662735156795]], [[1.0, 0], [9.243106963581958, 1.328958150436872], [41.25819786542339, 12.114499944181476]], [[1.0, 0], [0, -3.9103728985111204], [-47.0, 0]], [[1.0, 0], [5.668767862471924, -4.912015314273518], [7.542686428484113, -52.46053641968943]], [[1.0, 0], [3.29542457423737, 2.855501648400304], [8.396575458123824, 58.39946507097503]], [[1.0, 0], [-0.7575132600881768, -5.268620450557442], [-58.52907139048434, 17.185685967327213]], [[1.0, 0], [1.3049051600581816, 2.0304720629029105], [-27.83280587112639, 60.94534368875273]], [[1.0, 0], [7.914778745074092, -5.086519442380453], [29.494465923133937, -64.58387167017081]], [[1.0, 0], [-5.888389198113215, -2.6891372420788917], [47.80483357800581, 55.169718927860856]], [[1.0, 0], [-2.9914993155791705, -2.592148912648548], [11.242872223589526, 78.19589390859369]], [[1.0, 0], [8.62356933794098, 2.532108421310443], [69.82404322498803, 44.8731878488146]], [[1.0, 0], [2.5881132315261874, -18.000722915912963], [-85.39487465169027, -25.074197558887242]], [[1.0, 0], [6.910427210781135, -2.029084506607524], [81.60159268462458, -52.442159293192965]], [[1.0, 0], [-1.5126901794754686, 5.151749640632693], [-84.9666068159493, -54.60472256301536]], [[1.0, 0], [4.970297353018786, 3.1942161537082225], [42.7877463391943, 93.6920955215154]], [[1.0, 0], [-12.235328457377319, 1.7591746520698597], [102.66574817675122, -30.145383582032977]], [[1.0, 0], [-18.362418413921564, 8.385835506140449], [71.37982000003608, -82.37670360461415]], [[1.0, 0], [-6.357647319114939, -9.892692329208735], [-46.94189646921317, 102.78841547506057]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-483-161.34-c1-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/483/2/r/a/34/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.2090146453313156, 0.08856998778340601, -0.03769494804121144, -0.1706865936552676, -0.31002467262372313, -0.45330926872444444, -0.5957602820615305, -0.7302232463756037, -0.8475098450286294, -0.9370453295427446, -0.9877994202530166, -0.9894671277848764, -0.9338398381722616, -0.8162704261415883, -0.6370968239709094, -0.4028544355666322, -0.12708678572954557, 0.1694372216892998, 0.4592666293269036, 0.70968655112821, 0.8850440126556983, 0.9499091086618168, 0.8728785293414136, 0.6307057804609167, 0.2123339646099885, -0.37766901244472867, -1.1167988751569335, -1.9639146846593303, -2.860526596542999, -3.734265903038104, -4.504488658186852, -5.089683230972705, -5.416065470988252, -5.42649213470589, -5.088645532456873, -4.401378213969146, -3.3981840697280603, -2.14699344608004, -0.7458658016797767, 0.6853580170793604, 2.0168347618134397, 3.122785702309214, 3.8962668661394066, 4.262787191588979, 4.190881298129368, 3.6979736464280175, 2.850367051241808, 1.7569072361488398, 0.5567324001922009, -0.5976034538358156, -1.5595756819230833, -2.2081174170791895, -2.4642662561801942, -2.302493346401323, -1.7548176161935416, -0.9067892843469161, 0.11437905891223288, 1.1580262399020778, 2.072028780642674, 2.725275850790345, 3.0271352368446056, 2.9407663460412836, 2.488033871081234, 1.7450962264531173, 0.8292812161111234, -0.12064098328610658, -0.9674895120081162, -1.598063240413501, -1.9409815402942716, -1.9768170470904, -1.7387188112013936, -1.3034602818248815, -0.774648021116153, -0.26134906909654104, 0.1436723085948741, 0.3817846439195542, 0.4387908214007872, 0.34558712456758445, 0.16903003050388507, -0.005076549885917451, -0.09322818949467855, -0.03503630344750825, 0.19110186279026461, 0.5612157907355371, 1.0097395297666423, 1.4437683141191076, 1.764717745040713, 1.8926329275390676, 1.7874886376459183, 1.4621575022678128, 0.9833134904632803, 0.4591117297393717, 0.015527086739331267, -0.23392024696913752, -0.21834604749452743, 0.06769707479499587, 0.555018628076171, 1.107796407509883, 1.5487098758041564, 1.697113751047733, 1.4127321332139224, 0.6353338473143479, -0.5891706476723221, -2.1036131089897, -3.658803826039703, -4.9553450064500995, -5.701054635162387, -5.672966401316467, -4.770929815258784, -3.050616197459901, -0.7272650254174937, 1.85281356055254, 4.269251214506665, 6.103101151588512, 7.016238535805397, 6.818554752837324, 5.508660439778837, 3.278833093299024, 0.48217395423372844, -2.4321386794146655, -5.002731495194453, -6.8420114282754225, -7.706553153102761, -7.537445301397385, -6.462588242428603, -4.7611975355208465, -2.7989893878935077, -0.9488278438436414, 0.48546333450859525, 1.3255638949646027, 1.5437747612127488, 1.252729469016518, 0.664006876595152, 0.02711447428813417, -0.43545654831800634, -0.5811038606003783, -0.3755702991635212, 0.1087161279500172, 0.7222114373655534, 1.2863989101016158, 1.6466580560539767, 1.7152619328915464, 1.4930757772581225, 1.0647314341497602, 0.5695809412419279, 0.15752013292108658, -0.05705635121593338, -0.029519880223654267, 0.20263664385369556, 0.5330258134243625, 0.8212718583862083, 0.9391619423076931, 0.8140376718820378, 0.455918536684187, -0.04062442667136711, -0.521478730773555, -0.8184201859406288, -0.8020142138022428, -0.42615370531330243, 0.24988282472127754, 1.0699459166360537, 1.8194499251640548, 2.284064573329287, 2.31238123447438, 1.8641304240181242, 1.0287369506852095, 0.006904137048126935, -0.9415562473769942, -1.5702459266582445, -1.7188291474771318, -1.3643293418915934, -0.6345998199362367, 0.22234456564540617, 0.906813568595385, 1.155875811768903, 0.8268550251227705, -0.04916235325980918, -1.2617173266895902, -2.4683751089043793, -3.285162444262886, -3.3969612677209264, -2.6575097536801207, -1.1496664888365473, 0.8139706363593389, 2.7543830276989274, 4.1400140494269895, 4.523037419819829, 3.6622034047453242, 1.5984575948342912, -1.339016299506381, -4.600630225602442, -7.542587657549594, -9.579818274840777, -10.326206161341524, -9.685487424726224, -7.869062449922539, -5.336444204087468, -2.6747890645992136, -0.4501582139181061, 0.9297012462718244, 1.3051702868890953, 0.7850711283138204, -0.3049273489703045, -1.5282931059437286, -2.4660133350962954, -2.83042430092001, -2.5333190458241557, -1.691752899221349, -0.5738588115043524, 0.4955253164807279, 1.238702926767254, 1.5064775621881865, 1.3135665049311651, 0.8199618718733734, 0.26737395160165567, -0.10640959158553948, -0.14646573364738885, 0.1723379130586485, 0.7442423035271105, 1.375514452632772, 1.8550501907532801, 2.027651792939201, 1.844904956778672, 1.3769945391829785, 0.782720764339412, 0.24959364446843518, -0.07384052467845403, -0.1288962444271191, 0.037344448150865434, 0.2964700242002683, 0.4939937966171234, 0.5142861955498887, 0.32996606838927994, 0.01567651933616025, -0.28100144985237197, -0.40258487691873895, -0.2560089065878711, 0.13062200748397496, 0.5935978789183789, 0.8726163290525404, 0.6954876006593068, -0.11702207587107032, -1.562035759185205, -3.41543581801402, -5.26339191193335, -6.603009774381476, -6.986847858898225, -6.168729842319576, -4.203691629496976, -1.465529849663813, 1.4311597020568347, 3.7881675145832268, 5.017614907585009, 4.8158992683986614, 3.2637339069687994, 0.8183438088099496, -1.804591799977085], 'positive_zeros': ['0.21334890079575942156576420652918', '2.05402915280856236756701453645608', '3.04914741969912868240961060805889', '4.81476070948183934092942069239141', '6.05866103428851907669086622306099', '6.98647203400483448320464141001399', '8.108722175218979813968329977348804', '9.200211469677056654052916759251962', '9.870632124332468744239218571865787', '10.15220450073513948744040479538781'], 'prelabel': '2-483-161.34-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': -0.9397681607483953, 'root_number': '-0.9821505120481563 - 0.1880967083272445*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.469884080374', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.21334890079575942156576420653', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.05402915280856236756701453646', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.04914741969912868240961060806', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'bad_primes': [3, 7, 23], 'central_character': '161.34', 'conductor': 483, 'conductor_radical': 483, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/483/2/r/a/34/5'], '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': '2-483-161.34-c1-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-483-161.34-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': -0.46988408037419765, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.21334890079575942156576420653', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '270451862151777400142089614878', 'Lhash_array': ['270451862151777400142089614878'], 'label': '2-483-161.34-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/483/2/r/a/34/5'}