-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_1480.1403', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.984807753012208, 0.17364817766693036], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.6427876096865394, 0.766044443118978], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.9396926207859084, 0.3420201433256687], 'algebraic': True, 'analytic_conductor': 6.87309110492009, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [37, [1]]], 'bad_primes': [2, 5, 37], 'central_character': '1480.1403', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 1480, 'conductor_radical': 370, 'conjugate': 'dirichlet_L_1480.1307', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^1', 0, 0, 0, 'a^49', 0, 'a^2', 0, 'a^24', 0, 'a^43', 0, 0, 0, 'a^11', 0, 'a^10', 0, 'a^50', 0, 'a^39', 0, 0, 0, 'a^3', 0, 'a^24', 0, 'a^18', 0, 'a^25', 0, 0, 0, 0, 0, 'a^44', 0, 'a^16', 0, 'a^9', 0, 0, 0, 'a^21', 0, 'a^26', 0, 'a^12', 0, 'a^23', 0, 0, 0, 'a^11', 0, 'a^14', 0, 'a^34', 0, 'a^51', 0, 0, 0, 'a^31', 0, 'a^40', 0, 'a^46', 0, 'a^9', 0, 0, 0, 'a^37', 0, 'a^40', 0, 'a^4', 0, 'a^29', 0, 0, 0, 'a^25', 0, 'a^14', 0, 'a^20', 0, 'a^19', 0, 0, 0, 'a^3', 0, 'a^26', 0], 'euler_factors': [[0], [1, 'a^1'], [0], [1, 'a^49'], [1, 'a^24'], [1, 'a^43'], [1, 'a^11'], [1, 'a^10'], [1, 'a^39'], [1, 'a^24'], [1, 'a^18'], [0], [1, 'a^16'], [1, 'a^9'], [1, 'a^21'], [1, 'a^23'], [1, 'a^14'], [1, 'a^34'], [1, 'a^31'], [1, 'a^46'], [1, 'a^9'], [1, 'a^40'], [1, 'a^29'], [1, 'a^14'], [1, 'a^3'], [1, 'a^30']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1480-1480.1403-r0-0-0', 'leading_term': '0.906290092453083395716618907690+1.34529051724178696349449495049*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/1480/1403', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.6220876386494325, 2.635079580784044, 3.5179804589096593, 3.3280159037361283, 1.8263917706647406, -0.10445641328665975, -1.1207821838901308, -0.5883707017561443, 0.777174438866975, 1.529436743739676, 0.9297538863397253, -0.20821341909152383, -0.29554181247867434, 1.244524544483178, 3.0650095002389737, 3.0793405440485264, 0.7338812879630311, -2.0912639792055554, -2.814169879992403, -0.8913036632285649, 1.4524304883561596, 1.5329243712217249, -0.854309748872516, -3.19927244212644, -3.111620887645582, -0.9807391929352387, 0.6669943295710241, 0.29890668228345674, -0.8931632485224142, -0.8169477437058223, 0.5491580349864011, 1.036198794218496, -0.6604214944990842, -2.7950277556658256, -2.4744354020390658, 0.4813811313992614, 2.8102309503156992, 1.5779915215487974, -2.119259658920279, -4.354316399256939, -3.118461478190127, -0.58014108856693, 0.0015952719746154908, -1.479254898717329, -2.219513714907302, -0.6852309628608867, 1.2196318688941994, 1.0042791716795296, -0.7276287440864204, -1.1790358160698269, 0.41409378523084006, 1.5216400840923825, 0.16612022921532432, -1.633962702552545, -0.23982572924087692, 4.282558143429594, 7.477891834853373, 5.925463481133734, 1.563339079782641, -1.0147573832150898, -0.4644619219820734, 0.3759193343209215, -0.6444244665339575, -1.7950854027987981, -0.5467135791780122, 2.0953097022458778, 2.8500018518969203, 1.1151210395688778, -0.16015686493878448, 0.7781565764745638, 1.5190314520616637, -0.7289581012849775, -4.174988796250574, -4.290745929730921, -0.3369401337903634, 3.091593709930555, 2.194106392025524, -0.9810053926763707, -1.8446737848393018, 0.16407905260593894, 1.444241042893155, 0.15061890994637528, -1.2797801933576083, -0.574424891002408, 0.5712223687550343, -0.38908254238576867, -2.113937033851544, -1.223273930021881, 1.8698477595673868, 2.8228002324262773, -0.12720875119943323, -3.083084996464428, -2.1374795378808304, 0.6916901205597938, 0.5573776352839572, -2.734106935978867, -4.436111495724039, -2.1126834937283787, 0.9292220936996216, 1.0415840924524473, -0.4979403268801906, -0.4861658052688222, 0.6007548067853475, -0.06754855218400062, -2.0570643588170068, -1.9034361011591907, 0.7171627308868291, 1.5395335513540485, -1.6556263184976372, -4.834710572516809, -3.398817657837785, 0.7472232104211001, 2.043598512288566, -0.3227637922420715, -1.714250215385365, 0.21159801891522395, 2.0370809135117605, 0.6365722896302106, -1.7168627939085372, -1.4991349766283208, 0.18148040007129262, 0.014936291305841166, -1.4077394482676642, -0.7913625226064009, 1.449111149462693, 1.2858877743262922, -1.7127786721536917, -2.5483725905855636, 1.4596062821904254, 5.693701697561868, 4.767684711003976, 0.5257277993422709, -1.201131066751119, 0.47829544767403753, 1.3046905224335203, -0.270465152751554, -0.906851048996614, 1.032519124060343, 2.307290319446422, 0.6536126588738579, -1.0278429903253583, 0.15066932715530706, 1.777902906627519, 0.5199972942053267, -1.4432887101115688, 0.1193613507316224, 3.5178532062233456, 2.9095297068257757, -2.1551658187212324, -5.308673679672851, -2.9356349310205356, 0.7579119359228824, 1.0132071007712595, -0.5225500680625411, -0.16409614956333402, 1.026803474943495, 0.08036097787945429, -1.4983724976157122, -0.14025576227791003, 2.8541169965588242, 2.9764908650521553, 0.3592032186784278, -0.44865259791195494, 1.0923235366503177, 0.057259825082392024, -5.031147929869758, -8.390602171483785, -5.701902902107955, -0.9960934985068467, -0.05731437278914882, -1.6310492189632373, -0.9466165233586803, 1.587835340934587, 1.7956978833707944, -0.31578230497043647, -0.8621920654701136, 0.5381514560170377, 0.5360342591440614, -0.7137653306698144, 0.8653319059694604, 5.160783155487198, 6.400053909288329, 2.4716976832092965, -0.926510184742772, 0.6751524989568826, 3.4592809501359887, 2.338104100208087, -0.3915546110847945, 0.3075787642384401, 3.1057257711323536, 2.94911361535913, 0.08382632260920019, -0.889698881110385, 0.5490537598600831, 0.6780797796267788, -0.8502263519223616, -0.6828467304809248, 0.7271351797437262, -1.0030330521399096, -5.4377676471150656, -6.209945053192875, -1.324873973408347, 2.842913437370497, 1.6352122380742746, -0.8255426575604141, 0.44882295517027065, 2.8160025183572555, 1.5657020685009917, -1.4300486142604298, -1.5865372492899203, 0.05404277173736594, -0.3971025563846585, -1.8172695411435462, -0.4735750343746712, 2.1997456717102892, 1.9185303360393902, -0.18414995116519853, 0.36864202150077097, 2.2488176538463267, -0.09769182417962467, -5.770772505474471, -7.3231566403124, -2.744963501325324, 1.2009536196367492, 0.11686213320992524, -1.963649031558058, -1.083212941714804, 0.15584187132598812, -0.8865452055212804, -1.3053345054971155, 1.1302105883230498, 2.7839341670164033, 0.7841657659087049, -1.2766488257992021, -0.12111636489189449, 0.7773286706214423, -1.960122767431681, -4.217755057136435, -1.3537421306213322, 2.6430741121398524, 1.3559665741877318, -2.9246707645794277, -3.177660805291395, 0.4513195774434088, 1.9070819459257098, 0.12655141501714123, -0.569392336141051, 0.4145359813659572, -0.3736354689396399, -2.353523539535633, -1.5350973796200162, 1.0365383015966678, 0.4293020035029239, -2.5763630581897856, -2.28102442725285, 1.10828468475264, 1.1627871029137573, -2.9955208741566124, -4.5900996086588295, -1.1647657619001837, 1.226518693819917, -0.9170824562158858, -2.836869243492747, -0.962556018000021, 0.9608742651066867, -0.14864016704050287, -1.0445730714858368, 0.6457037174365033, 1.575586559252758, -0.0705356027967256, -0.4742810470587645, 1.6672937254764733, 1.1728563577684972, -3.8692522205033963, -6.771852412607548, -3.055493636442838, 1.5256394783057177, 0.7468705322088303, -2.104583705701123, -1.567058748460263, 0.13360375776516775, -1.2100283870458677, -2.9438224833079008, -0.949544964478597, 1.9933357505091465, 1.48280223464638, -0.408377995775188, -0.13172766682844783, 0.07059515824458598, -2.2019855626778835, -2.82121619019528, 1.43620680543929, 4.958629683552089, 1.9032753757981349, -3.1520481386584898, -2.666389151644412, 1.3347961987384458, 2.076743094216109, 0.1743314956893815, 0.6748098516834972, 2.524203346364145, 1.3049586772799098, -1.3933893622050513, -1.1709919451999058, 0.40121851523278584, -0.4533928739379372, -1.3742425521747108, 1.3432073101551245, 4.191132589057739, 2.350718863827415, -0.6564745446414566, 0.7210933971961508, 3.078134787903732, 0.10891694139349609, -5.034161257671041, -4.684969785217392, 0.029054260337032147, 1.9472082845507785, 0.3287661182370344, -0.25683455613181566, 0.0830204215847939, -1.6967329999582974, -3.3717993910655655, -1.2388016914036093, 1.5839159774364555, 0.45475955697284953, -1.571674313460706, 0.3514470023010568, 2.879698497238824, 0.7965452166348582, -2.1190859264531023, 0.3998065738224126, 4.977634874398072, 4.351103246598787, 0.3389714712476593, -0.2904352050447766, 1.774856495420064, 1.2576019853983926, -0.9821395803308507, -0.786073123175131, 0.33791146663122984, -0.8660208793897731, -1.63579153655162, 1.0968743663826896, 3.166519774761046, 0.7939477260524959, -1.0338862548112793, 2.4924155800663095, 6.058081722342195, 3.365492790507103, -1.3360671050087207, -1.250380528550308, 1.011401083722873, -0.09081319478195023, -2.1194972864106996, -0.567890847518481, 1.6129904913394055, 0.18489040856046837, -1.8817129626619244, -0.8953763565016906, 0.23804308781051994, -0.946641788063386, -0.7467619385726942, 2.0448782068630824, 1.4585938698089713, -4.326938261261501, -7.408234876640909, -3.3365007791499504, 0.936685587210833, -0.37369494020363175, -2.5367034464081426, -0.8214263304028409, 0.9023494046232818, -0.7233286216162318, -1.7847567581608272, -0.00543861075782924, 0.2866390887689594, -2.418561271385885, -3.1975267289809497, -0.7493634181586022, 0.08255530760850659, -1.2177272952904188, 0.14564844212940503, 2.8073948099335984, -0.11016167103457192, -7.116043380458022, -8.749979056027705, -3.480156226728684, 0.40302944228989057, -0.17940322038947987, 0.09811496409488767, 2.522927947986361, 2.359191895243695, -0.33976587627427146, -0.7420753496168792, 0.5795600000333541, -0.5423096205423781, -2.164052650241972, -0.11943591688296609, 2.2004904645507044, -0.19933461918091225, -3.310746741024441, -1.415911169141361, 1.3382483948824726, -1.142279210701944, -4.58718416609552, -2.3731981539084672, 1.7176666835314245, 0.9226268973497345, -2.0868925792407316, -1.6315297090415888, 0.21930884690466235, -0.390148520457781, -0.993975662781077, 0.44185371412799224, 0.1337891025622993, -2.677287272382707, -2.1518808795086293, 2.595050346633142, 4.225682976079664, 0.7464961141073357, -0.6621701092965195, 2.141985402705915, 2.2648709767048576, -1.9679747140724966, -3.273251362368701, 0.43435229421783583, 2.437594453574315, 0.48297943926977294, -0.2094570802926092, 1.413239203659654, 1.0205663075688975, -0.8142013527309346, -0.005910806436743805, 1.3433198080657784, -0.9143480512706534, -3.2169352985411495, -1.0429734734815872, 0.6607774213537898, -3.5754066661771695, -7.9001202306135045, -5.036532290947612, 0.37603937388942443, 0.7502184906191453, -1.2977864831186579, -0.4273987317793467, 0.6802459209956249, -1.2110643846309466, -1.9888963393153256, 0.959644928441787, 2.6874335777086364, 0.7267684865788077, -0.2577801781640252, 1.1262812114342904, 0.5877561768246518, -0.837350204422808, 2.573177978697299, 7.975878582014557, 6.4650361186587135, -0.6228789366773146, -3.361930995535947, -0.4836115955638417, 0.5481170110184643, -1.2913763370218998, -0.7300793882543982, 1.4496783003354758, 0.6830164912650731, -0.9105704787989967, 0.725002498454131, 2.3504517614377827, 0.37649205799615293, -1.0510805208770497, 1.0066013771549385, 1.4646761405347541, -1.7753703569627721, -2.200584240402569, 2.0140534755385975, 2.8636352526544244, -2.283001313178183, -5.081207023957955, -1.7990274106949669, 0.6607278019528068, -1.0581123186035857, -1.751099502968013, 0.20241612175206675, 0.4405662862118988, -0.7128360768006718, 0.7772849500087491, 2.6308696587327147, 0.5680987455899161, -1.7352397355777116, 0.12489571404389024, 1.2029570345005218, -3.0555304098306917, -6.351089538572223, -3.041431298550022, 0.8985395800949496, -0.15500305364990352, -0.9671719031465913, 2.6884461499476346, 4.996686818338526, 2.045853158228336, -0.7330346778874142, -0.023588422153851346, 0.1330780986663871, -1.2354052203396444, -0.3027115888175276, 1.4840206112549101, -0.2806808748883449, -2.195661208588776, 1.0345257177192404, 4.425811326117248, 1.1462233525392302, -3.6906493089763117, -2.288410069021723, 1.4512469671304102, 0.8144824969393413, -0.7329836419831193, 1.5610188331066672, 3.2414803150872546, 0.43996564340185806, -1.894798496348511, -0.4659527740626468, 0.4581850026248425, -0.5095246313432423, 0.7441261453228329, 3.1353201147633625, 1.6388637785887332, -0.891375061034019, 1.6426965829131706, 5.220431845074892, 2.7250848797458547, -1.2997348206455235, 1.0933449167561362, 5.75205009414865, 4.634489512289716, 0.5652938793551551, -0.18634575383777927, 0.2986955553364876, -0.9295351180482337, -0.19698337526692125, 3.411121246688759, 4.02675342612425, 0.7588337974704273, -0.2824789619026784, 1.3824196917134377, 0.8241131599361773, 0.035567004625450066, 3.971814723558661, 7.563740107117173, 3.405813777011492, -3.086189510605556, -2.590172680297933, 1.6709472012309716, 1.74749380981672, -0.37556015446921653, 0.1857056985921982, 0.6006309440714268, -1.6141741440088109, -2.094258089612479, 0.3193364842653615, 0.3537761593049952, -2.0040567877735453, -1.2142651843558325, 1.142012835874455, -0.8127830788673017, -3.75800107161541, -1.0171043307718177, 3.023923279384843, 0.9356697932320927, -2.794080157680003, -0.8023487878678568, 2.7841373784476637, 1.6594880825855447, -0.3607107435896965, 1.1306666554551348, 2.0054734992607415, -0.326716131712106, -1.3569599875502703, -0.02485515092384439, -0.35358223584523185, -0.6257704023363626, 3.5730441294938826, 7.381753666833716, 3.939209531719731, -1.5323056369711496, -0.9655796237234895, 1.556838921621818, -0.5373120593417904, -2.7178788387902157, 0.175658528303801, 2.680718396708066, 0.2993232886977874, -1.6091489722298444, 0.18000691906436334, 0.767629499526401, -1.1251466761454894, -0.8563746414817017, 0.8391665931928723, -0.30691444744974705, -1.359816018818367, 1.4942256066792932, 2.533532156472314, -2.6736951570167187, -6.250195608591742, -1.956533268639378, 2.778251462312492, 1.3004024043787303, -0.8441168181416945, 0.7684010479937552, 1.134497305252033, -1.5479193032761862, -1.7573550744229514, 0.6826957050271742, 0.2547396407791533, -1.8966809171789765, -0.9768257290005328, 0.3346372467003619, -1.6407463536962168, -2.3508028690384823, 0.7402344199137362, 0.882060142919922, -3.8521405367399257, -4.594546996018796, 1.1271883608513524, 3.8042566483796003, 0.1111420916650736, -2.0027710478356875, 0.0010183701214053638, 0.20632705463798537, -1.7221454401387872, -1.1271511850673177, 0.21110773330563212, -1.1219675852324418, -1.1244121225439148, 2.6471490541294442, 4.031945759815516, 0.629188881169463, -0.9905832113394135, 0.47480091690405934, -1.3457569653971397], 'positive_zeros': ['1.543364902249438142488393585905', '2.326406858945280284358238786550', '3.37001832768475625744435028416', '3.838553331358040788738658861096', '5.074204472345536618784582008581', '6.04170426346343942651892665912', '6.78147754916050379575532956176', '7.95811145991751082237274755682', '8.51218426222985469579574425678', '9.25715863653935900846409929794', '9.91065889969919956927677667425', '10.89275833456252066536150494666', '11.70313525188222974786200906312', '12.94131218880388037928807420492', '13.12563574698103108079200477223', '14.157351794427264538565346314415', '14.86984815918457644856549713022', '15.5581157997085614072927930178', '16.27306337248407891659268312254', '16.89604521067190383590970504996', '18.26316972740435538862326025743', '18.865168765270175791646192899023', '19.238266395366341155329572777888', '20.06558624710078437545035723333', '21.15254004343641866258702162474', '21.37404107214164916696679702996', '22.120089848534194387264867752834', '23.14771267064588637604073543025', '23.95978746537929970741919904649', '24.66558394196719664949209132868', '25.33638538500381671339414779417', '26.05749290461027492014876184050', '26.49476802198562783440265069637', '27.31622698396671381259630809263', '28.11478872429463099622708326607', '28.97242426094814378773886238457', '29.44122905268254297557022363483', '30.505659310342154836488721007954', '31.13851810219268800442479973894', '31.6898574458951147292699938626', '32.17569418109059988965506383234', '33.04330306207823110659721221925', '33.62168917859338808140742928369', '34.6257331346900908221027968414', '35.27656665035729606127924085680', '35.913140851955871402390562389531', '36.63589505666790343078722887477', '37.4554391249040282817262588173', '37.81599655425962009184351410059', '38.54690696238680639541378949511', '39.20846173913833978133417538093', '39.91192499638073924391921038364', '40.98406714804476767757645686817', '41.49098873548673926561774035111', '42.14193834552470589860609144900', '42.67537799449114203217980346946', '43.52339584592627103845803684925', '44.040641046393672476562610728366', '44.752317559097192681405714069219', '45.30138634696309601934871775184', '46.12848027214794641044263932647', '47.1033239388536049847622276341', '47.68867766508813052223082583971', '48.16090054909516002041716264844', '48.76278871875417805622720287832', '49.38978893626064600976898393072', '50.36325668218359029461609799192', '50.72954421968029751901330579259', '51.25499899634011238164980751582', '52.638036960168421567345316251731', '52.79589753521148750195074238378', '53.55263613510343494970577355756', '54.326586201499811679277752284017', '54.88337450314549062087559630539', '55.43131485856307762819099948671', '55.850465530159459440256521861329', '57.05393405750140741602584256456', '57.43324621113110264993197425017', '58.37300386805935470979669123194', '58.710526502604424625413452887421', '59.69780289781116356044151035102', '60.20299053640019854859290788253', '60.765565237043572388659456785046', '61.37984482815264971844468409583', '61.77995449304352130262191983433', '62.88487866794509126380260763186', '63.607111756130332108701036127339', '64.01042075331149534508157116189', '64.83754147537503393947535082942', '65.60890473671784420679298775825', '65.84873286992454773715523175087', '66.61350744748289296706053424331', '67.46075229084700231321677180739', '67.75216674220758717538032601924', '68.43136565971764290610855745711', '69.54749327034244132584840394428', '70.01359666041247511420457586131', '70.84046103595224296302747279094', '71.047277218870655285538321819247', '71.75584508607413708146443991181', '72.5841077587453478225116227102', '73.14395524428478687678823737087', '73.56842076714372966340831752050', '74.46220444545216499422832949329', '75.0962225014725231734876341712', '75.89828190360508650470619575418', '76.58374886538486584461217413084', '77.04969953144725561953699147521', '77.43663759011821345279676746694', '78.296066711507400989683357133678', '78.79677780671628021380097370182', '79.58114553872208554577833393076', '80.1026017923760153282763346539', '81.03214034206159532311718131113', '81.470439094990224418325122082157', '82.29779388410127482643256050590', '82.78728664797084216217323482622', '83.34363924929055041639871476212', '84.05059716270645449484893929914', '84.46009471650719243209472378714', '85.09075648540704690584876960373', '86.11374722689205225264847276127', '86.63480212368653662253238363869', '87.44347296371954450845515562880', '87.619657518756037116710395105065', '88.52144986327659971975067098164', '89.28183276137404626416733785077', '89.72900040403987469720758930012', '90.01744827742248343784874693805', '90.85367242908127989290953327527', '91.66488219437084182284342578538', '92.3884021883586028085979164617', '93.18284919096175854921553829655', '93.28572119361389512821718718432', '94.197440228401785773011396815170', '94.88718884754722058275354716325', '95.22875116181303387543100998853', '95.82447988216010392711457716517', '96.77158488743352048338354248372', '97.11113861599317410772872324211', '97.81869058077770053544117170179', '98.74788249935568464429354001160', '99.44345993088259616410857416842', '99.82047265828334008959182299136', '100.03837655384129193982470677895', '101.046244581365093480693454267063', '101.61396167796475298450977822039', '102.155034707785392678296334896940', '102.87596948667780820295869871147', '103.41177073114421758823794074664', '104.41261029368994350401194729669', '104.736352558756490454711763936287', '105.472721475512213392257995326478', '106.10394459767784604857693048091', '106.40655059937114053197989874941', '107.09024326811946962629904621358', '107.88737846962290055345529931617', '108.26701593848794202487545756909', '109.26368931485629598948480706200', '109.83506976047853885286044630472', '110.30156968519795293462351711481', '110.9977345280318905385237736521', '111.58349965326675935560251210256', '112.354558982527238315084670881947', '112.60697564168093656379052639749', '113.218074935025759020180797969495', '113.84570511662714218885707722537', '114.8904368007275728696473913235', '115.273748238098182092274207892455', '116.03319841703288564752144645759', '116.46449005403176607373946280824', '117.188381180715095764461162311837', '117.54587726097864655958563302124', '118.55998454837291700250302915771', '118.77543784250985837466052421234', '119.36011460154901155832186229638', '119.99451747405866551838143540237', '121.17961767825540131036757544927', '121.51598137973107737904758192174', '121.8585101358962078282767467686', '122.767633252773247677253608575434', '123.27748227611219401629060766270', '123.67088554064913400022063071496', '124.38601636790288163491436568770', '124.984805630325262405782700200104', '125.74314461940147589308410281899', '126.164778737783173036717881711884', '127.03121916482079991819991841543', '127.5857035759136372142929728450', '128.37401540812917275578082334436', '128.65770887350774127500082843203', '129.28722691042561067550004153584', '129.70572974646664350152780550959', '130.46369693760877815445948492872', '131.31852022738734751984511162641', '131.6597620614491031394756193367', '132.36465886183696013093000872751', '133.09255168115088272336710472872', '133.827186808933379522312469406614', '134.11393617037610326846881658779', '134.83946796107073183520300338227', '135.31340457043863019904207039802', '135.8523459860782782382883866626', '136.66488389388172776769618241064', '136.96621096589870162336412838688', '138.093654278303896880029549687384', '138.53724021691086530348723159300', '139.13073460196220313259058176369', '139.52926348052133163013604847919', '140.227598555476647017075737243156', '141.04997800305576188715663722432', '141.326459203036850808336805820711', '141.9635933495842362600424017150', '142.33123830283502913467206431574', '143.40788329825253841471120406270', '144.11597038794209162864494367869', '144.47815210435555653090803949845', '145.09290162138840678263480543623', '145.72173266671925349642445435205', '146.16234986994660356959972083728', '146.91813242032298693187924381510', '147.37719120652267700444347931655', '147.96875144564511095904820758851', '148.61214830932279474166667607329', '149.25374746910446335507746938132', '150.155298832436533773381957783114', '150.48149809255785853329358292625', '151.216109490265244356600304821695', '151.66120979332666184329806848025', '152.08916756032953719180069697625', '152.86485547541320079780939270948', '153.424017222671405754997545685966', '153.875249224697531486026610679908', '154.88837450359669101811571026370', '155.29203953052249835071753369511', '155.73983064694546541974885126910', '156.74213463590471365448213677411', '157.19344546941339847146845072418', '157.5334025357203925285083832943', '158.1655395541034441800016625895', '158.72159235689296910644826763223', '159.30805186444363141791941286444', '160.06028508217377702445966627569', '160.79046015920047951294764089323', '161.35630142513644868529649513686', '161.71557712477033492845824358367', '162.5370079825497797329663686121', '163.20112419016114412852912851947', '163.58498740173273958018462478944', '163.96549484434508930768545298864', '164.84308873090909720389594091687', '165.18654354524856944429868534795', '166.11037969501464143892246619583', '166.49183262851812345157601788847', '167.57709447872626440877295084733', '167.878325865311153411677032700185', '168.22874756088329963053804290905', '168.770940800823751074683449180203', '169.778872758785453269073333809108', '170.0631751980269999158092458242', '170.78670515285486241821943682738', '170.9288648878205880159935440130', '172.01763805878076306892605290556', '172.67627869549569245217545506938', '173.35636523586650496281192062572', '173.70929356666148585669548727721', '174.170960055485739956325823206433', '174.95589768090952437293079982770', '175.36196625714421652409709704096', '176.06806349038325045841995901500', '176.49327904879655380782565453105', '177.24905688760020332740536231392', '177.87432096460058121310044368356', '178.49397560650882589925480068424', '179.264140935607389531156992429632', '179.52112645569483624190644083901', '180.2740122716244857355305263769', '180.94560224710797279845112795671', '181.152934685868052145740449540896', '181.64074327376250087199505340732', '182.698395668642721810997445137594', '183.215878879243019830449248990269', '183.70313929752292220051679230908', '184.36188111296658756408990239952', '185.02761617256272222480074436365', '185.599697046605758914037805262026', '186.071762104737633918470550529187', '186.69375796993184455158208965538', '187.14360420778966009421382445609', '187.6818159765601836341254552977', '188.30566458854500326631306960049', '189.15941858820125003964726565132', '189.817180647276669955620442821912', '190.20484192570254116303015184584', '190.767801192809790769313505877', '191.46420255294061304594718206231', '191.90862864956677206448794412411', '192.651177209356117231051577975131', '192.91057336589067531303737908911', '193.67986027882899392781661379117', '194.134338134113622278370929883785', '194.94354320557420016418768244065', '195.63300693477125847453978640017', '196.24984410860353495616821284744', '196.59828248800988611255774656754', '197.38948289477436681143548946499', '197.606740298769561146354332470751', '198.23759848818515592520799013785', '199.11946047451825494778020908227', '199.57503121845797979892000984229', '199.87398731260184724383452154744'], 'prelabel': '1-1480-1480.1403-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.87309110492009, 'root_angle': 0.6225865798772152, 'root_number': '-0.375667661129788255894233982973+0.926754448805763531279963952625*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.311293289939', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.19836581702338697261200169775+0.403140605822905267756820942839*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.54336490225', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.32640685895', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.37001832768', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 6.87309110492009, 'bad_primes': [2, 5, 37], 'central_character': '1480.1403', 'conductor': 1480, 'conductor_radical': 370, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1480/1403'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-1480-1480.1403-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-1480-1480.1403-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.87309110492009, 'root_angle': 0.3112932899386076, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.54336490225', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_1480.1403', 'Lhash_array': ['dirichlet_L_1480.1403'], 'label': '1-1480-1480.1403-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1480/1403'}