-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_147.65', 'a10': [0.36534102436639504, 0.9308737486442042], 'a2': [0.7330518718298263, -0.6801727377709194], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.07473009358642425, -0.9972037971811801], 'a5': [-0.36534102436639504, 0.9308737486442042], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.6234898018587335, -0.7818314824680298], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 15.797343944809878, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '147.65', 'coeff_info': ['x^42 - 1', '0.988830826225129 + 0.149042266176174*I', '\\\\zeta_{42}'], 'conductor': 147, 'conductor_radical': 21, 'conjugate': 'dirichlet_L_147.95', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^37', 0, 'a^32', 'a^13', 0, 0, 'a^27', 0, 'a^8', 'a^23', 0, 'a^30', 0, 0, 'a^22', 'a^17', 0, 'a^28', 'a^3', 0, 'a^18', 'a^25', 0, 'a^26', 'a^25', 0, 0, 'a^3', 0, 'a^14', 'a^17', 0, 'a^12', 0, 0, 'a^10', 'a^23', 0, 'a^40', 'a^27', 0, 'a^36', 'a^13', 0, 'a^20', 'a^37', 0, 0, 'a^21', 0, 'a^20', 'a^11', 0, 'a^36', 0, 0, 'a^40', 'a^29', 0, 'a^10', 'a^9', 0, 'a^12', 'a^1', 0, 'a^14', 'a^7', 0, 0, 'a^39', 0, 'a^26', 'a^5', 0, 'a^18', 0, 0, 'a^28', 'a^35', 0, 'a^22', 'a^33', 0, 'a^30', 'a^31', 0, 'a^8', 'a^19', 0, 0, 'a^15', 0, 'a^32', 'a^41', 0, 'a^0', 0, 0, 'a^16'], 'euler_factors': [[1, 'a^37'], [0], [1, 'a^13'], [0], [1, 'a^23'], [1, 'a^30'], [1, 'a^17'], [1, 'a^28'], [1, 'a^25'], [1, 'a^3'], [1, 'a^14'], [1, 'a^10'], [1, 'a^27'], [1, 'a^36'], [1, 'a^37'], [1, 'a^11'], [1, 'a^29'], [1, 'a^10'], [1, 'a^14'], [1, 'a^39'], [1, 'a^26'], [1, 'a^28'], [1, 'a^33'], [1, 'a^19'], [1, 'a^0'], [1, 'a^41']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-147-147.65-r1-0-0', 'leading_term': '-0.0977140746539499451065843757100-0.698883910460136154845465059504*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/147/65', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-0.705681770124133, 0.4228249194932099, 1.4077894914625375, 2.097558363669908, 2.3338944529294015, 2.037781330351635, 1.2940712553966625, 0.36907711814097943, -0.3696389905037952, -0.610369973229605, -0.26130367674235094, 0.4698426196179467, 1.1455834051336353, 1.3106410571960865, 0.7523981461438314, -0.33474649595509265, -1.3993411602679322, -1.8090238926141988, -1.226785720570128, 0.12697268579087434, 1.5114039018958425, 2.0324557855048964, 1.1683674512365494, -0.848766165548453, -3.0557991765395434, -4.229602084298304, -3.5724194132616685, -1.2121042299284663, 1.8096835048098385, 4.094586544034251, 4.677734185270317, 3.567556271861105, 1.6877252799870723, 0.25138227333754765, -0.023452663665199124, 0.6680768402575298, 1.4467747861138576, 1.453593418734518, 0.5124917919548839, -0.7416051529901747, -1.370633802717025, -0.8926400173420095, 0.3021224437714872, 1.2273659390242821, 1.0808289091733927, -0.08177969363037031, -1.3462933915125896, -1.6700259757427591, -0.7970500270290468, 0.3947116471541117, 0.4743988087372295, -1.4032953116221267, -4.672087319911993, -7.548348750786358, -8.201293423403998, -6.073355601244654, -2.344826299239833, 0.8541624546800469, 1.9247701028330635, 0.8616150970399967, -0.9030778154516512, -1.718434787786212, -1.0055776644964252, 0.40580549916575304, 1.1168604310230996, 0.418954523743923, -1.1128074320222594, -2.178183056456467, -1.9351969171146601, -0.7373620113586953, 0.23547490604069957, 0.10379329084461283, -0.8796479601698349, -1.5891989909960367, -1.1628519323814601, 0.05240435570422254, 0.6999515000649494, -0.3239630045310279, -2.665378098557445, -4.546103896593811, -4.162328512031279, -1.306687945101787, 2.24496866140989, 4.0413060404866314, 2.9278880597771684, 0.00468611543663938, -2.2876844142302466, -2.1936548018111592, -0.04131189602312378, 2.17326502098041, 2.5959919876581807, 1.0815730866352558, -0.8468504613684004, -1.5089996554939387, -0.5839038451779108, 0.7636511489120545, 1.1667680698164347, 0.42325262526831364, -0.40545916674643145, -0.21039761579607216, 0.9208393755372396, 1.7477032696134533, 1.2013492534816361, -0.3701250290849639, -1.388209483357644, -0.5899271452716103, 1.582553822461667, 3.2322955561354645, 2.806078115514187, 0.7404935954339644, -0.7432256975196797, 0.3312188381722958, 3.6954274088573458, 6.826931405746356, 7.0723456270387235, 3.999953817091033, -0.2009048103028096, -2.6481552119755998, -2.2176293701252052, -0.26356495597251606, 0.9356325887958425, 0.37758070771487223, -0.9563362097771045, -1.421179233523608, -0.5427957027300429, 0.5660869343425747, 0.5566966393123443, -0.5788448248867342, -1.4516291071065828, -0.811924764437418, 1.0079609549662127, 2.3620842078407063, 2.036861806597941, 0.5837470443449886, -0.28257899805399467, 0.34129934258144823, 1.349318560424614, 0.659680739565619, -2.4291688048583144, -6.034656898166326, -7.113658882490918, -4.31780920849107, 0.5218459390932619, 3.8676673103279104, 3.585107328478904, 0.7115064486024592, -1.7739711499443584, -1.8609850905528633, -0.18509704583682562, 1.0553662477458114, 0.5975717455216154, -0.6634893071784063, -0.8986045215039942, 0.488190854185906, 2.1831656062305758, 2.4634945372692707, 1.1210462847980387, -0.36784915902903836, -0.5750500280722661, 0.2693129235707694, 0.6631847510883394, -0.23312617783205852, -1.4152529041664799, -1.1165011857001041, 0.9634516530419892, 2.891201595316963, 2.336222849413958, -0.7857053436707805, -3.7972243459493233, -3.705356313609315, -0.23508743283284547, 3.7342508277616497, 4.907190905701903, 2.7327037700069696, -0.24051536891382921, -1.1049505359900098, 0.49947666922894135, 2.3081730725011793, 2.071990826799909, -0.057339608150652206, -1.9093753594776148, -1.8086627776496427, -0.3062709039263284, 0.71437936253537, 0.32855747357680476, -0.4864829309049199, -0.28031866586791643, 0.909685720015108, 1.5195626530408415, 0.43827012537786325, -1.417544648305849, -1.982613416530208, -0.49974931267780365, 1.3603385585082712, 1.2463574177855108, -1.0878888077809696, -3.216071083399471, -2.597849057810461, 0.4383179754714373, 2.7072300590459673, 1.4063222711414003, -2.820838138223292, -6.363093611415464, -6.236677732353989, -2.987269393595832, 0.12228708985354762, 0.5945772161895156, -0.9887284611274678, -2.1395597478573634, -1.4688057700284631, -0.0070816036996421555, 0.4465955626310484, -0.30697085239183014, -0.7118234023897736, 0.4092613967441543, 2.19175193012227, 2.676446675707035, 1.227636572845745, -0.6035407544733441, -0.9262265940811261, 0.15983525666515422, 0.6898440080036684, -0.6099896357646389, -2.467281142302717, -2.3992779005102163, 0.10623746487490138, 2.3942562933511837, 1.2170439716583499, -3.544753718719235, -8.2589718066739, -8.985768787064405, -5.388443948590981, -0.9014646988314261, 0.9298510892766192, -0.1502084649961045, -1.5477307781811889, -1.2019292902477066, 0.18098594514782562, 0.4506184186230413, -1.0455024856233215, -2.6054956775889817, -2.337343431003845, -0.5202266309627136, 0.7937607218824094, 0.35921218794113063, -0.8030386276151456, -0.8840990096142618, 0.2601752827402324, 0.9108149221820772, -0.13601123061358816, -1.7181352838660158, -1.59331912052115, 0.5155345712678057, 2.009732195811493, 0.19704100300734606, -4.262143965701875, -7.471637090729005, -6.248035270615636, -1.5830205926235177, 2.369732181161509, 2.7137123839352073, 0.6604848544630662, -0.29625814512613696, 1.4374694280067442, 3.916844550034604, 4.244346266906682, 2.0479410259459314, -0.29202523365792993, -0.6597101799530326, 0.41715000895377696, 0.8333611241525397, -0.21578073133683182, -1.31851343355592, -0.9313690381721252, 0.44618702064445115, 0.9612312242543767, 0.04363317100217689, -0.6173789306007296, 0.7371578432523109, 3.331685795340233, 4.40937049544614, 2.582602148908235, -0.1711531061428211, -0.6540652113761117, 1.6090333066598967, 3.497503028633397, 1.8655669021978398, -2.5323929821832345, -5.539096178815434, -4.138278915433288, 0.18802348978714695, 3.169105332570765, 2.4378769925665114, -0.2584468153174605, -1.6122328257262954, -0.6618173998664701, 0.6241254562705421, 0.3304984620680198, -0.9595206896161859, -1.2791134939219484, -0.15784934725195496, 0.7208493811843352, -0.07431877988668892, -1.5958643385092535, -1.6523286835954814, 0.23000624889141352, 2.018563079797755, 1.7559469523304152, 0.1541770333408911, -0.35685507100350367, 0.9594269526585132, 1.8362772590637313, -0.12172201493861755, -3.8214924823638325, -5.176766312967041, -1.6734624536437859, 4.315441293129989, 7.670999074516781, 5.8907054280119615, 1.5156292949081587, -1.053774073173758, -0.39504730435491275, 1.080886920432453, 0.754982268266424, -0.9651498758504387, -1.6867770462483989, -0.5289722208726074, 0.7054549866417579, 0.08268869989563214, -1.789797161542491, -2.588915623410398, -1.4070839613301018, 0.09057393996494587, 0.012877711974688988, -1.1808392324317072, -1.455366524331281, -0.2538222509969352, 0.5182200251214742, -0.7917461389124074, -2.764822214105647, -2.161869343741061, 1.8408808297075616, 5.846245249355609, 5.677058645417123, 1.2591378591120657, -3.0478993260563945, -3.3053430259861516, -0.29421797470967753, 1.8263919910954869, 0.6563443907473583, -1.8698418360296956, -2.354880366796249, -0.2874500088425879, 1.6279598400451583, 1.2054277575115464, -0.5139722512742051, -0.9542740184239331, 0.4764896447989803, 1.806825962218965, 1.3895170645332318, 0.08468172542851143, -0.2363546155648284, 0.42339998690613795, 0.1584548285853437, -1.8565315051797922, -3.661110600492576, -2.8250562113915363, 0.10996104683844844, 1.9156878144179204, 0.7575597532944784, -1.1928620212375587, -0.3699963031360632, 3.3890743855144727, 6.112007093996424, 4.336584115865496, -0.5151908334672248, -3.5998996233796206, -2.267578499610218, 1.0592631931557626, 2.1292683837234225, -0.03984351100853884, -2.492556380989935, -2.442872370496414, -0.5617374348171021, 0.5335604003656873, 0.004296958779339606, -0.4572674485148637, 0.4732075721154308, 1.6189083293475104, 1.033448509184633, -0.961290343719712, -1.92767718402563, -0.6198332088190981, 1.1939024808463123, 1.1076728551650403, -0.5580022067146999, -1.2150060982383883, 0.14477192374135678, 1.116265374557781, -0.9727013424964619, -4.8902313141880525, -6.208751492494375, -2.6370872774068737, 2.658518780797376, 4.295680052495156, 0.7943078831193359, -3.882730938572214, -5.127427718329379, -2.743869047764833, -0.25011211272595707, 0.008989497094952939, -0.650560493444927, 0.05964678475845059, 1.809442905266358, 2.1951549638100105, 0.35907186989019085, -1.6288861938683208, -1.5767262983804375, -0.11861286936381052, 0.3674823753531939, -0.7594329732409819, -1.5677064282247906, -0.5437122351041942, 1.0219885296852875, 0.9126190196483497, -0.4588587766405698, -0.1944116691727913, 2.8897032647296177, 5.740364583554913, 4.303101586824077, -1.142633215563974, -5.602563064521316, -4.960047433850795, -0.7344946089850328, 1.9658037134033999, 0.6330149698346157, -2.1294244574885317, -2.5798749909900516, -0.7079095510185123, 0.29155869670635703, -1.2876953311655273, -3.4017129453507633, -3.2557667979829503, -1.0971733090134395, 0.4070233779950523, -0.011559823763212167, -0.7529122061937846, -0.08409007978190047, 1.1881997967474702, 1.0921491848965628, -0.2358139329397492, -0.46111413779938976, 1.4482434702231723, 3.269416411892661, 2.386277161802992, -0.2640312996981947, -0.9695384945403319, 1.7709302376997016, 4.768473900818437, 3.9789801820710524, -0.0951373707776194, -2.71346050537264, -0.8334381412860967, 2.977771027439582, 3.793646746230386, 0.5019852041878933, -3.059916761087485, -3.17361810577579, -0.645346571338684, 0.9322414992560909, 0.1018455741278334, -1.13422983732681, -0.8024901675392593, 0.19569056150187844, -0.15055310409871062, -1.5962839502417652, -1.8843752086741863, -0.23448897051122877, 1.2468839909594656, 0.5329894983624102, -1.2699807305567112, -1.429379515514103, 0.34726499721337023, 1.2841344575698093, -0.4407014390566619, -2.756927019495823, -2.4599605053448332, -0.15355005412473674, -0.19336936502993562, -4.97408299555474, -10.995059605966398, -12.373536061268492, -7.726635767571054, -1.701971027587565, 0.678117000385752, -0.5201018672755571, -1.51777784030134, -0.38416282139634356, 0.9355902636079999, 0.23142952827626945, -1.4935140116115297, -1.639174795766815, 0.028157988276227595, 1.0612095421979466, 0.033509525896078154, -1.3383448587471434, -0.8016016087137768, 1.0336243592405783, 1.6079953143354455, 0.2586745647211689, -0.8484063837901976, -0.2042277836158657, 0.4595915344556396, -1.217376770497774, -3.94006639532622, -3.477678066215382, 1.7028919445947213, 7.4520952351221705, 8.324256595802972, 4.135491544771362, 0.12992772005263992, 0.4355222393594254, 3.327411755547439, 4.2134577690355535, 1.8712975977610677, -0.4709703625442431, -0.08123328231680926, 1.5984243650437764, 1.4497390334823927, -0.6997243744207994, -2.0240254638765114, -0.9354836893662785, 0.7722948750728009, 0.8040568668062789, -0.306936349120613, -0.37969107892874493, 0.7846982292879147, 1.0904932088841321, -0.2966603091055282, -1.160221419411123, 0.5933266340083407, 3.3079941166333287, 3.3057133279451447, 0.10141135932769048, -2.3889840818214423, -0.9697291648448172, 2.210369210304755, 2.246613526759944, -1.856668136436694, -5.529295097489881, -4.461271663741721, -0.15016109100980896, 2.2262732557903377, 0.5439439193417025, -2.0168020833108025, -1.7663079917528655, 0.678533469889838, 1.9351915036403127, 0.8447636452719874, -0.39646234647720335, -0.01622307302501528, 0.7497037048203333, 0.02891705117234359, -1.3881138980498187, -1.1467323117736188, 0.8324200754131115, 1.8676929084280172, 0.4402436798712006, -1.3493722070481868, -0.7596612943777334, 1.4366472976547329, 2.01026265165882, 0.2871974251897853, -0.4292351594848491, 2.284836061597977, 5.60226759065283, 4.399961593517154, -1.7984843152556003, -7.391743262135712, -7.212891400351858, -2.6017540799277312, 0.8121015589443334, 0.28935061883335683, -1.4797188862993835, -1.097494819753989, 0.8496905606176179, 1.4465466515934633, 0.16524617199472758, -0.6084203808842347, 0.38686197296690333, 1.2091699347155738, -0.1919700172590198, -2.5812368283522558, -3.060193642958568, -1.271002241882729, 0.24454577840374553, 0.032831309394294114, -0.18404666567309286, 1.351869234598197, 3.031084662767954, 1.9710677283607447, -1.0796764297683095, -1.7376692557545856, 2.091478531288346, 6.485965192297293, 5.910254454528337, 0.4025277333979056, -4.2011688718290365, -3.524589511198072, 0.267946545872696, 2.063718389439983, 0.622407646686898, -0.7087021009871095, 0.4422835237525001, 2.1176462349460525, 1.4050420395805867, -1.0008433368405782, -1.8804429218322756, -0.27434872340918864, 1.3230775610440495, 0.8728288246340797, -0.39420656287363176, -0.39710442114093814, 0.29159026008086797, -0.4410874868922641, -2.337805568879127, -2.5893092297471596, -0.1625245095823325, 2.0502371176910223, 1.1908725038501002, -0.9989957441333939, -0.2066012538696023, 4.080802881954394, 7.063176211741117, 4.7731138695223505, -0.41192740857659743, -2.7669367728577985, -0.7635989673940519, 1.2490361463956694, -0.6247874923176568, -4.5033185983229975], 'positive_zeros': ['0.192666614528067454616038348107', '2.324735105353978553366930406191', '3.24724983823265663132867724974', '4.59882982292419355818734294288', '5.91138050284395234779467838149', '7.06943150459538057468194183704', '8.56290325790506621740904436959', '10.43124813650426495229936268755', '10.645923298992077821147191198871', '11.99864595676947919489620226265', '13.050179549067002742394174527055', '14.04431836277752854465257726769', '15.194906849597995617941295519685', '15.74284401243159009690563822021', '17.711249199462100553573709372368', '18.58546389434196818313133932234', '19.59479039455782952018965655376', '20.40458167255031790007496237786', '21.767367484113678588814893354263', '22.230055155884823488456022836527', '23.42385543374043156938315778418', '24.004544122031524890282932150308', '25.42282534123802479461810322140', '26.56298377653443620610427964392', '27.50501492335061133654795613355', '28.600881064424852834476541250074', '29.50116246247805956551312706354', '30.44552051079711312029971845070', '31.00935613739250214127612888623', '32.11712692616979823335976513971', '32.90806827860864385357303216183', '34.175919146698401736079200366506', '34.64268669806920091814814220061', '36.23336187096797031373210837690', '37.23224895704031128915026158908', '37.90140151074372724875373114237', '38.88418727859857761664575864167', '39.54729588557423585103050287787', '40.46222867428475275790456874586', '41.71142322758291290503137067935', '42.0846963602080155025462594679', '42.90020009077395277434673030088', '44.34066930213681450200032693857', '45.384013153382129473372340331638', '46.28222194507369691287825247828', '47.019156908546568914574536694682', '47.72761443270315509275504960905', '48.96544732622600333871197676349', '49.59744639021666541012076567795', '50.25646027636033913450816173957', '51.12469633762104646020460763746', '52.11996994375731209773260855078', '53.14179897038138023876102980754', '54.34328859394167304607393538943', '54.92710179997493513627509086782', '55.93005968382390186358398186965', '56.93902252865098385495631062744', '57.610885159198648310228842504915', '58.21120247646554684654859587249', '59.13552132367236557249831924074', '60.07320971279227633064232239505', '60.81226755087513659406728787947', '61.83386255888201500801227490325', '62.61757452793405946947808862883', '64.0439393233403803099471136632', '64.51522513841394934181686314976', '65.626879753408882061448050233231', '66.14581323004069379485620847399', '66.79739920483071478795618412688', '68.00477414445369163470922903423', '68.70882727885667224716442751143', '69.270916753593943507286987674417', '70.30153672774549333164149015878', '71.03509265335237402511420036506', '72.59175830443366685401165813097', '73.09796817837320256250004545218', '74.01656446513704700793565614882', '74.5018753456662271569683786766', '75.714410316299867843754241816', '76.34251629485723934150426395522', '77.12397617319480594007061047754', '77.78700071415955138811953162242', '78.68334837101974812579382079856', '79.3917302599706970648268058002', '80.72726656467655637215735359605', '81.68163186848531296962257122147', '81.97564233296255871134509080803', '83.38382409425729950747394021682', '83.95112248916932014380392920414', '84.639647906853392027112647531465', '85.52258801198669127831686185084', '86.26152385965441812349169036387', '86.7625598249589388463599786615', '88.09994557424704103195673074836', '88.557069035430552118701814391250', '89.516800451934174834048643880056', '90.61161894436805276534956749057', '91.53088342489927423710108227514', '92.32092544785327746041450158224', '92.89661310280378955711281255879', '93.786638463340359518312673540291', '94.359450166948754309713847719943', '95.28110435684286265075493281276', '96.28552858560942610222729589669', '96.681624196188831963613339493240', '97.488585168174264272806039556156', '98.52675474614202977584242504209', '99.82195760414897766144819912731', '100.38482034586387432367022084704', '101.080987616432730570229821602502', '101.978660256126081137620701534489', '102.51593677978705515934672849289', '103.72042160213241231941294394162', '104.06676374786566168664929220009', '105.05844746730627426429174476918', '105.49375001062077334649726491421', '106.43941305447586923839527860833', '107.57587967541222188459486212162', '108.465951925230842395700094133047', '109.14119916294715716291180426133', '110.03551299432608454210796274931', '110.83906129217015123902564788198', '111.479284284003598646674377735', '112.52678430222955182096058718978', '112.937775792259642796431970151395', '113.47386654744776453450780447672', '114.67593955725267025988470080166', '115.41636483350562872810819485876', '115.97735309888107179528037766695', '117.15451224691863684224493488247', '118.01914065475649850982315149337', '118.74579237695201370470293149118', '119.79242843141928523309499340654', '120.31404387806915698324699324875', '120.82462583603681153726798222916', '121.73008538790011244709995034033', '122.59293637368293371512451959962', '123.33702089333394608622128119851', '124.03695169849092610012275987017', '124.59341031304213915383866106320', '125.77244621110922003690154735944', '126.61117172600311563128672133435', '127.87937257104491292004270220985', '128.129252762091599114245012795934', '128.73786679470532511403332801114', '129.734125631674481872007635475767', '130.65415560667193797264298594867', '131.07327845254024198823771838741', '131.97081657123074915261285382239', '132.70242457841537542390057590270', '133.15545469622441623852067782670', '134.315606975816545158887711188691', '135.36837460953654386398214222197', '136.00540232147607115256058118828', '137.00580916593420211342656276919', '137.29599559838138625207390336647', '138.616820249295555961909826900376', '139.0588506426981376866667779538', '139.70711665086046774367176020132', '140.567876030919288267248446643610', '141.04366223176383599053983067720', '142.153153189618890172759427509940', '142.64790501890273371434273842142', '143.74299113707192551267077140100', '144.44213705785371663926270034892', '145.34915627802766030512377601120', '146.33332796537600409288705419097', '146.89579399609002687226047640107', '147.72995862855235541557110224040', '148.08229194490220272326708303814', '149.09840133056167825641786825721', '149.777429329224691814868514590410', '150.57002210489260753506593558244', '151.19624809324944362929370645786', '152.2140023648401350394670468686', '152.4732291699532385949371849506', '154.2084625936089479463844187054', '154.59441132118457500216233187143', '155.38139354011583914227379200465', '155.97940574503583563649647275266', '156.87017195348252974451025611287', '157.50622190606287956085021891876', '158.26328878511363122807588839755', '159.11146006032839007380004064037', '159.74277851974401277303274288436', '160.14616231407305243047885404406', '161.166098537068513019976034997576', '162.5211610666019272953923850767', '162.74430063245509115245888471297', '163.96845017481487784973067404104', '164.39061492069558140186602907723', '165.21950746125742030985942075334', '166.089121769056191659880444151738', '166.78309965094957382329219971612', '167.30391181292412421819990982773', '168.06986802669366123232333747092', '168.680845295994652159077954056563', '169.69615490005630465043250113913', '170.403605564836764960304612874080', '171.129720125789872741064248771037', '172.19889109331342333098270849809', '172.86955668759451613093604155802', '173.66598539092450690367462528649', '174.54780912242579926306147052851', '175.00516435452642695935553899386', '175.63117232857144909880854441759', '176.44076651761995244613974718351', '177.249865275546432170045580986329', '177.92370440763057317051546008738', '178.79936747559291805723750092323', '179.14968737795060899349119183252', '180.23319223036552451663777192503', '181.4475944998879177965288801887', '181.92112447684102091383216766921', '182.67580722165337369093368394426', '183.47327049059012651086962514377', '183.97525182355447983549820577193', '184.661793538950458645798440943684', '185.85153849814514908730307974131', '186.26528736127132670260786052015', '186.63099147322826297427025097488', '187.69955644747473752307385089241', '188.301466133591890305341137915924', '189.395432820687655686989119045611', '190.28913341427557042920154937674', '191.03615614747952941367275423438', '191.49020495561742840979686998898', '192.36994303462522418062509346375', '193.165171183808013190517643376870', '193.94767500908667656170320307528', '194.52908222307471922585478820414', '194.902381482780256861853143191874', '195.95442187565986686700894896466', '196.7158768758974070081492606641', '197.20810739619710689133956420634', '198.41028039822610056275833320483', '199.14487518322743827805063574404', '199.63047813539483467046905642673'], 'prelabel': '1-147-147.65-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.797343944809878, 'root_angle': 0.9115646258503401, 'root_number': '-0.961653436841036269604700736037+0.274267510674930409921979613715*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.455782312925', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(42)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.922487008411362929825309284550-0.474344202338798417647267007129*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.192666614528', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.32473510535', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.24724983823', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 15.797343944809878, 'bad_primes': [3, 7], 'central_character': '147.65', 'conductor': 147, 'conductor_radical': 21, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/147/65'], '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': '1-147-147.65-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-147-147.65-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.797343944809878, 'root_angle': 0.4557823129251701, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.192666614528', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_147.65', 'Lhash_array': ['dirichlet_L_147.65'], 'label': '1-147-147.65-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/147/65'}