-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2304980721136417652452698822975', 'a10': [-5.450603835795164, -2.657082152562822], 'a2': [-2.2997328098939542, -1.437032550483052], 'a3': [2.3047638586534096, -0.6608804017325306], 'a4': [2.3469661521767624, 4.8119937178645955], 'a5': [2.2237715758180876, -0.23417937266877248], 'a6': [-6.250047714069001, -1.7921723427816711], 'a7': [1.2328013531659032, -2.1352745793230077], 'a8': [0.9506769583587265, -9.045087060056712], 'a9': [2.3310292502915244, -1.4565887369113506], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.79289409601082, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-2.2237715758180876, 0.23417937266877248]]], [19, [[1.0, 0], [-0.38834511760443996, 4.34156516358246]]]], 'bad_primes': [5, 19], 'central_character': '475.6', 'coefficient_field': 'CDF', 'conductor': 475, 'conductor_radical': 95, 'conjugate': '1439150551538746646669647712550', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.2997328098939542, 1.437032550483052], [0.8767422935781548, 1.797588092598334]], [[1.0, 0], [-2.3047638586534096, 0.6608804017325306], [2.544144288469278, -1.589757792699615]], [[1.0, 0], [-2.2237715758180876, 0.23417937266877248]], [[1.0, 0], [-1.2328013531659032, 2.1352745793230077], [-3.5, -6.06217782649107]], [[1.0, 0], [2.9292390450951395, -3.2532495424089767], [-1.1498130959441881, -10.939740849051006]], [[1.0, 0], [0.17354725971346857, 4.9697432857108215], [-12.968332653377715, 0.9068341586736289]], [[1.0, 0], [4.8750779879747235, -0.34089866167505556], [16.834557168606697, -2.3659427163211126]], [[1.0, 0], [-0.38834511760443996, 4.34156516358246]], [[1.0, 0], [-3.202318895708134, 0.4500565705860615], [22.109019006581335, -6.339659183790982]], [[1.0, 0], [-5.338180182165504, -0.37328192171886143], [28.71777399350554, 4.036019927841898]], [[1.0, 0], [-7.593543111553341, 3.3808632163905847], [20.743048797124604, -23.037489589799222]], [[1.0, 0], [-0.5862317667233228, 1.8042358574135342], [-29.933628791873055, -21.748054334821507]], [[1.0, 0], [4.188561779239754, -5.3611146002616765], [-9.918797719586376, -39.78212477731586]], [[1.0, 0], [-0.7223825411907084, -4.096834972664106], [-40.406782693794064, 14.706866163003756]], [[1.0, 0], [-0.5291167483729216, -0.036999447359635], [46.5425992308538, 6.541135745123076]], [[1.0, 0], [-2.6221520258865234, -5.376208371880073], [-32.63005819225989, 41.76456994115626]], [[1.0, 0], [1.1564527581684518, 2.86232101833975], [-42.441048219980416, 40.98484385708084]], [[1.0, 0], [4.501514016531046, -0.6326465373077879], [58.63696345223745, -16.81387870483695]], [[1.0, 0], [-1.7998087098715505, -7.218638457564562], [-59.157488721548106, 31.45459470665468]], [[1.0, 0], [1.6257302657923594, 1.5699494685398023], [2.477864265877569, 70.9567487183558]], [[1.0, 0], [0.16300839638362224, -4.667949726083311], [-72.82217566896718, -5.0922225833211465]], [[1.0, 0], [9.151227985991767, -2.6240723990100085], [66.99579959635766, -41.86362187442319]], [[1.0, 0], [-2.3395864668685546, 1.0416510068095297], [55.53784032778523, -61.68102051462372]], [[1.0, 0], [-5.7474475503120255, -7.356397398490486], [-21.531048708370427, 86.35631963856369]], [[1.0, 0], [-0.1605693508367846, 0.6440084908464035], [-85.64591650731592, -45.5387415902314]], [[1.0, 0], [0.25207037422142176, -0.09174611315694016], [77.37048875501678, -64.92154857834048]], [[1.0, 0], [14.549244582659552, 6.477741037769854], [68.9204524549624, 76.5439170241716]], [[1.0, 0], [6.539850143820535, -11.327352722983797], [-53.5, -92.66471820493493]], [[1.0, 0], [-11.16509704450662, -1.5691520581681642], [104.77752485727676, 30.044471784052913]], [[1.0, 0], [-3.5234725771537945, 10.844133544394696], [-91.41892036436906, -66.41973350904946]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 29, 'label': '2-475-475.6-c1-0-29', '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/475/2/bc/a/6/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.1873760881677902, 1.2834065920286093, 1.3795028278446106, 1.4728132906822942, 1.5575433829446954, 1.625418046830793, 1.6664836820443165, 1.670129576244881, 1.6262599968926947, 1.5265783701513445, 1.365940233448496, 1.143702366571059, 0.8649576300803907, 0.5415114011341746, 0.19243496150612216, -0.15597011305892095, -0.4709404515262635, -0.7148486590878953, -0.8476543287308466, -0.8301386820850795, -0.6277458512845534, -0.21474355077822418, 0.4216834189091657, 1.2778662224715647, 2.331101951174252, 3.5385869556246328, 4.838213050421374, 6.151454892317611, 7.388368934759589, 8.454476724880132, 9.259043752461865, 9.724022220844892, 9.792737948207991, 9.437302713908672, 8.663751568724496, 7.514055645437066, 6.064443984979614, 4.419862750739228, 2.7048675165335365, 1.0517282386823572, -0.4130391991718335, -1.5821843872253987, -2.379606887979764, -2.7690223931936524, -2.7581278724486995, -2.3975010702294224, -1.7741411675240077, -1.0002963788455683, -0.19892485662316892, 0.512313345568683, 1.0363315788466099, 1.3089689400435827, 1.3065791063585979, 1.0476723213927637, 0.5883072108156282, 0.011902470924801713, -0.5849509780065918, -1.1084070392767629, -1.482403387243867, -1.6603107273382494, -1.6312178349636761, -1.4197857199356991, -1.0797393669720758, -0.682231630733791, -0.301294759948228, 0.0008060357897755691, 0.18542311647990353, 0.24417364749908327, 0.19896681260407056, 0.09532213677112829, -0.009692884376236936, -0.06235731426176236, -0.026720153588108555, 0.10484519007629958, 0.3077138546028638, 0.52917037058437, 0.7003827478056875, 0.7540789951975805, 0.6442685821400224, 0.3634613342652359, -0.047133998143146526, -0.49790789343018976, -0.8631852508569384, -1.0046296326645245, -0.8021484430521685, -0.1865908001342756, 0.8326379889375208, 2.1517581622023587, 3.5736991642237625, 4.828322729653334, 5.610362349119161, 5.629886566825832, 4.666988335490026, 2.6206691672771476, -0.45798939872080896, -4.356152505178102, -8.716985443536286, -13.083816179765721, -16.96457565143455, -19.906128652739877, -21.565628752682976, -21.765938704290345, -20.52460621461569, -18.050507601995594, -14.708230375269215, -10.956401710246888, -7.271235514308773, -4.06949257087386, -1.6451655350420984, -0.13142612331732798, 0.5057667236270623, 0.44245249720298624, -0.05368527307282518, -0.6873525771030149, -1.199404342625931, -1.4169325895424305, -1.2797617929594671, -0.8390355694306681, -0.23003353279325636, 0.37282348877964444, 0.8069821469922873, 0.9660069210184897, 0.8263989015537286, 0.45095452348090176, -0.031320811207978985, -0.46278189733166625, -0.7018613025771192, -0.6629002934875495, -0.3404609680296347, 0.18835760220072925, 0.7842289637964225, 1.2831332662257815, 1.5410770534933442, 1.4739543622020808, 1.0816963553520464, 0.44997655121154234, -0.27126795070792925, -0.90695115166286, -1.3031538525020303, -1.368077985121981, -1.096353048899341, -0.5698196077201999, 0.06567422617445066, 0.6412393200860161, 1.0123405755191617, 1.0992315891304454, 0.9087183108830875, 0.5306060288110267, 0.10932090120714949, -0.2015494802951897, -0.2887559458088802, -0.11815861969295109, 0.24949555043592397, 0.6718283353287211, 0.9648249188601818, 0.959137269658071, 0.5567067515174311, -0.22948776461713533, -1.2659714748660982, -2.3250295563790293, -3.1419355502140083, -3.4888657680353203, -3.245098636048343, -2.442429087007887, -1.2701015139893603, -0.03389344685875869, 0.9233070537943353, 1.3204226637250038, 1.0303521184573072, 0.1386570837006109, -1.051016633310118, -2.0716288047665605, -2.3985936717322303, -1.5833193917846684, 0.6182362253950561, 4.155753003322979, 8.659450358952949, 13.490627929452142, 17.86010728912484, 20.9893350399707, 22.277212310252665, 21.433083538247267, 18.54368670093441, 14.057539425081767, 8.69027157339741, 3.2736561781484688, -1.415464026086952, -4.805993490460713, -6.6289134465865125, -6.939572725757834, -6.065593032802565, -4.498585022285297, -2.7608428274514267, -1.282309355735898, -0.31763191582681327, 0.08000554404545175, 0.02836402063787405, -0.255442692930115, -0.5420760801731203, -0.6653057668531731, -0.5645897289905297, -0.2860850196382882, 0.05285708371196796, 0.31944869968399353, 0.42004502537313504, 0.33432519837034547, 0.11836279887711978, -0.12241081895808748, -0.27849593782414395, -0.2817188067412946, -0.13294532724366198, 0.09884856390993073, 0.306254587263815, 0.39091688341712966, 0.31061849349154513, 0.10700766786490157, -0.09873805745989275, -0.1436909888736089, 0.11677593111590713, 0.7471710920164385, 1.6913632123981603, 2.7708326079309873, 3.7268300532095395, 4.296337083943116, 4.298701478478771, 3.703740154313922, 2.655629749099692, 1.4396206834195706, 0.3969316805741638, -0.1886408095432834, -0.19696524950980862, 0.26588569356519864, 0.8744487807821716, 1.1653799314840119, 0.675198410177495, -0.9040397273562687, -3.59863844239931, -7.099071353419061, -10.801194589372999, -13.938859762309656, -15.775868407525984, -15.805284404598275, -13.898910349604167, -10.361538273152554, -5.870517457640963, -1.313871564232255, 2.4300629238510636, 4.710800378944807, 5.260940024927168, 4.245642025328871, 2.194179393948726, -0.1643638444995398, -2.1117236108203, -3.135529177907628, -3.0533129780215784, -2.032905960469454, -0.5088911773587593], 'positive_zeros': ['1.81830917819265500838939918510491', '2.67238021813105759547696712620866', '4.96247565514301399100668812833286', '6.03265654940541161034510829795632', '6.87746641733940484215513023806967', '8.124593060091105336884383604558005', '8.736473323891309775380411144039812', '9.033977837027460151004506807530868', '9.986811856939082498003604830231902', '10.65180180744226386152809658875407'], 'prelabel': '2-475-475.6-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.5908699129787623, 'root_number': '-0.2816144592589359 + 0.9595276422992186*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.295434956489', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.81830917819265500838939918510', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.67238021813105759547696712621', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.96247565514301399100668812833', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.79289409601082, 'bad_primes': [5, 19], 'central_character': '475.6', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/2/bc/a/6/1'], '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': '2-475-475.6-c1-0-29', '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': '2-475-475.6-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.2954349564893812, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.81830917819265500838939918510', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2304980721136417652452698822975', 'Lhash_array': ['2304980721136417652452698822975'], 'label': '2-475-475.6-c1-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/bc/a/6/1'}