-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1275.548', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.9510565162951535, -0.30901699437494745], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.8090169943749475, 0.5877852522924731], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, 0.0], 'a8': [-0.5877852522924731, -0.8090169943749475], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 5.9210751072791314, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]], [17, [1]]], 'bad_primes': [3, 5, 17], 'central_character': '1275.548', 'coeff_info': ['x^20 - 1', '0.951056516295154 + 0.309016994374947*I', '\\\\zeta_{20}'], 'conductor': 1275, 'conductor_radical': 255, 'conjugate': 'dirichlet_L_1275.812', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^11', 0, 'a^2', 0, 0, 'a^0', 'a^13', 0, 0, 'a^11', 0, 'a^9', 'a^11', 0, 'a^4', 0, 0, 'a^8', 0, 0, 'a^2', 'a^16', 0, 0, 'a^0', 0, 'a^2', 'a^7', 0, 'a^3', 'a^15', 0, 0, 0, 0, 'a^14', 'a^19', 0, 0, 'a^19', 0, 'a^15', 'a^13', 0, 'a^7', 'a^17', 0, 'a^0', 0, 0, 'a^11', 'a^17', 0, 0, 'a^13', 0, 'a^18', 'a^14', 0, 'a^1', 'a^14', 0, 'a^6', 0, 0, 'a^3', 0, 0, 0, 'a^17', 0, 'a^16', 'a^5', 0, 'a^10', 'a^11', 0, 'a^7', 0, 0, 'a^10', 'a^13', 0, 0, 'a^6', 0, 'a^4', 'a^16', 0, 'a^9', 'a^18', 0, 'a^8', 0, 0, 'a^2', 'a^11', 0, 0], 'euler_factors': [[1, 'a^11'], [0], [0], [1, 'a^0'], [1, 'a^11'], [1, 'a^9'], [0], [1, 'a^8'], [1, 'a^16'], [1, 'a^7'], [1, 'a^3'], [1, 'a^14'], [1, 'a^19'], [1, 'a^15'], [1, 'a^17'], [1, 'a^17'], [1, 'a^14'], [1, 'a^1'], [1, 'a^3'], [1, 'a^17'], [1, 'a^16'], [1, 'a^7'], [1, 'a^13'], [1, 'a^16'], [1, 'a^2'], [1, 'a^10']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1275-1275.548-r0-0-0', 'leading_term': '0.716435445934893244734766361021-0.437469591490641639228678816212*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/1275/548', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.8394399273747459, 0.49431633534566893, -0.2291789665845605, -1.1750308363952302, -1.665205268627282, -1.2129879538268917, -0.1536042147794978, 0.45566967144739995, -0.24350371072095903, -1.9086518614571133, -2.981165401923263, -1.9812074527522117, 0.9043649936836753, 3.5682474156556783, 3.6669759170099034, 0.8993928817272399, -2.386059691828072, -3.1602579618244877, -0.5765913364629668, 3.1170909854090842, 4.698007290124203, 3.0794561638936435, 0.21697081666378254, -1.1151017781530996, -0.21787114105110597, 1.136589444619932, 1.092434833637889, -0.053690042072901616, -0.4340669575221242, 0.8235518040787752, 2.3575468435788687, 2.288433558266243, 0.685836449043163, -0.4866213280962821, 0.023116254290111948, 1.0380752391300332, 0.5603427091702693, -1.3119349993845866, -2.225315930599844, -0.7705394525810128, 1.1035740000423286, 0.11379850691575798, -3.9618664891182798, -7.228069191554474, -5.927732613253589, -1.094369778201853, 2.3560945555595705, 1.3111230678799772, -2.0132427934468264, -3.0725090417859793, -0.6287523419897366, 2.1173636868439742, 2.0092741223218202, -0.12793119274284637, -1.123994584651132, 0.036475285698345496, 1.1883585099587088, 0.4997680762708196, -0.8598710522574862, -0.7316681321097724, 0.5757549018397372, 0.7280671135167438, -0.922690037498287, -2.0881900774287274, -0.8878525923146208, 1.181884605737034, 1.3693836778330764, -0.09631955586578057, -0.2593337351715664, 1.726590512141974, 2.464985308041011, -1.1147297526956077, -6.523371637868772, -7.83578232950463, -3.181741797519571, 2.5044438002546467, 3.5963646425003386, 0.6376127546459114, -1.231156647592171, 0.3549286622223415, 2.2809228882985075, 1.1684338990057503, -1.6347107584526295, -2.4162044508541705, -0.6677932766702943, 0.6363231914086009, -0.0672087942498628, -0.8058445211147152, 0.23781384759775218, 1.5582556085786559, 0.9044597765926818, -0.7611683771127606, -0.6596099145452188, 1.163561300404198, 1.716889831425702, 0.0367072189222869, -0.8604712517571601, 1.237997683054871, 3.6729954355379455, 2.705199130818751, -0.1490993421857489, 0.3962704304389531, 5.289651438070602, 8.588308314891423, 5.212554301633977, -1.7928570217174689, -5.164740579128852, -2.9070467329028853, 0.18872299668521308, 0.2823368144409603, -0.6644765757820784, 0.5285814491720725, 2.596137322405561, 2.140337037783179, -0.5230251335661309, -1.8041880758839945, -0.5391829374060242, 0.6296950803653841, 0.1068103642533321, -0.1474585687403546, 1.3772010677082724, 2.5371981281652296, 1.1117125936183765, -0.9179826181991619, -0.2739859912066407, 1.9494394188981001, 1.786289879217221, -0.7508533433360901, -1.101472728442583, 2.2021592762042514, 4.028421779835427, 0.1031104154568937, -5.627445845508886, -5.897102335415333, -0.5703667614022602, 3.234161568525224, 1.4948309102450434, -1.703845211729111, -1.378417682262865, 1.056120671224334, 1.323530950055373, -0.4719382651787607, -0.9150027363122293, 0.2801707296021776, 0.01663875853568198, -2.2596433034337795, -3.2641373009850843, -1.4892323083819607, 0.28217351700113313, -0.07572961722710403, -0.5976126556305392, 0.5678080858595111, 1.1993061619693266, -0.9884584270370318, -3.3424616967847, -2.0565951842705825, 0.9211913567832258, 0.36563400120841505, -3.3254444007427475, -3.89667310707207, 0.7190734770900953, 4.271858980175569, 1.5653898151225827, -3.2626121854341954, -3.005677786102329, 1.7007556808790225, 3.9909165967169855, 1.530551963763279, -1.0176267816138633, -0.4548320877337455, 0.5209296590570031, -0.7058389921109541, -1.9604378671982752, -0.8563486186019016, 0.4808085349252448, -0.6738162297649462, -2.5129748130044134, -1.917789891877937, -0.09232104091202635, -0.18863868632225023, -1.3624473632992409, -0.47022486817842024, 1.620559833538008, 1.2636495063569417, -0.7776787262896059, 0.19605808948239167, 4.130789161889383, 4.7679778031880495, -0.2682266148913806, -4.373341665363544, -1.6585490800645222, 3.6738286498670627, 3.8728609151314606, -0.4107852425486064, -2.0916104471855492, 0.548360459000552, 2.013466111634505, -0.40466132076369027, -2.5187248380419285, -1.0989323690531805, 0.9519683505628594, 0.45698317281867484, -0.7443883329256291, -0.2465500327859274, 0.09019156771262124, -1.7981459508620292, -3.4202873058170473, -1.896420231258578, 0.5488802330465448, 0.37724328181030625, -0.9963971756098287, -0.2778236655857915, 1.0941729305736794, -0.15424323180147645, -1.681140859725315, 1.4892885030285978, 7.218388060101044, 7.740206792920134, 2.0146391474480962, -1.7498505700366114, 1.1601367886057843, 4.7205582166263, 2.4169532859734133, -2.436887757542279, -3.0789484190553367, -0.340670457155456, 0.2506625463859673, -1.4594177757999955, -1.0805212187581508, 1.5521041621863296, 2.247844814983233, 0.3479077337087596, -0.4974887129732709, 0.565350382864872, 0.5408576850460614, -0.9207439431923706, -0.6959212160239365, 1.2220239127393908, 1.0227783319268802, -1.5994132587689436, -2.219522056868937, 0.2683080256259033, 1.4308848047359535, -0.2327984655866366, -0.17828439176093552, 2.877130079639487, 2.4046296771885345, -5.193228684288831, -12.334121581468123, -10.426034527786825, -2.782796135583182, 1.1136173010799606, -0.0009528759021982582, 0.14410047100391438, 3.0270199323607003, 3.7004693666571713, 0.9226619795289528, -0.5763871154243455, 1.0015217996104984, 1.7712294806957862, 0.0071491905162161294, -0.9446176996710803, 0.35424729805135874, 0.7474012525486492, -0.9322069533962319, -1.4892323247928139, 0.018842470808515623, 0.1813051399744122, -1.6689360246002296, -1.4045856444564189, 1.8352732555597373, 3.0203455423308045, 0.3497054256178496, -0.8936917069210644, 1.6737964509510874, 1.948737651301263, -3.8786527427759796, -8.852518866567381, -5.730929246237226, 0.7215971488137417, 1.2506847953252291, -3.278248714147921, -4.788934552990378, -1.7898941895088254, 0.09935061548749347, -0.7134976082961635, -0.3178016385086919, 1.7391039996290156, 1.5081540572336736, -1.1346449642262428, -1.9071735041277575, -0.222184558060502, 0.09712144804474203, -1.4668188460692964, -1.491333952635161, 0.09267901362280956, -0.03844524220002837, -1.2255669713644435, 0.3498894023716314, 3.3325626143968847, 2.5313730262950775, -1.0066558576598563, -0.8674836066139278, 2.8152193123336855, 2.8166383798747283, -1.7260696300393539, -2.523007191655327, 3.4000537117023275, 7.57944256609195, 3.9946789059929575, -1.2638325130740269, -0.9677529418161144, 1.9219139803143372, 1.5195039913078319, -0.5391579959021039, -0.03652857697122713, 1.2603300712194527, -0.02524322026507874, -1.6932099215518486, -0.5582647240618095, 1.0542871453873501, 0.17841653309571995, -0.7325854369426384, 0.9772854215873957, 2.4078926511742815, 0.7867152743188502, -0.9172687752486952, -0.15672925147702338, -0.10538914090046646, -2.4515306982763456, -2.20744119037591, 2.9791634790011803, 6.03030173708987, 1.4848978861119095, -4.201829712354083, -3.0248376547739433, 1.0934241562320828, -0.01731212879192098, -4.033945998652657, -3.0001232311817425, 1.9838773941816013, 3.1803979098045456, 0.0006175942657561019, -1.343377731429189, 0.3512724831685086, 0.7567789217053252, -0.5030726216106385, -0.0031811041923236944, 1.4676503416727913, 0.392627382995258, -1.7883798689320947, -1.1705694328197946, 0.7933288690168585, 0.28342201102117315, -1.1649919607846635, -0.24097128378750854, 0.6968831921082248, -1.6199572702181717, -3.7075148912584894, -1.5914525958398915, 0.48917456099902545, -2.2351910178420473, -4.3254334317546395, 1.3273084159353958, 9.394958818046568, 9.294514643375807, 2.3694122109758826, -1.2407610451314146, 0.385015623491119, 0.511075269605523, -1.9932541758040432, -1.485229830676743, 2.275040794991985, 3.3368458909715937, 0.7483594797154243, -0.5893075737006352, 0.26768041777746665, -0.16115157900745425, -1.5661514508261543, -0.8028214295851515, 0.6739426963191057, -0.5348891245129086, -2.2364899003486043, -0.601428902443855, 1.8631266271103284, 1.0823395070638913, -0.41840916067118594, 0.8721695873308644, 1.4111465863882806, -2.0555511641253794, -3.7757161422112153, 1.3704971141352607, 6.42187561065225, 2.751209702540367, -4.620106407997727, -5.153250789537386, -0.2562157886212812, 0.9284033690707433, -2.0275900243239877, -2.3574247022345025, 0.12439599339780988, 0.045326748397660474, -2.044439233284008, -1.3607003987064594, 1.0230573474358424, 0.621761471307291, -1.3427574573696932, -0.9610641161123623, 0.35922230002132194, -0.3350564712959727, -0.8242694626345874, 1.1881459747838996, 2.3341426167662, 0.3943289331370814, -0.35754257978065196, 2.352044708874033, 3.458872535314483, 0.554945784454309, -0.6866291146308895, 1.8884833803538192, 1.2158732229518872, -5.23819106234871, -8.247390870000316, -2.353221437569899, 3.6116022511226107, 1.3063517186014793, -3.6340933386750436, -2.9952967945822855, 0.4045181716050034, 0.6269080482470318, -0.31915206997066753, 1.0179370912139563, 1.5424719208682989, -1.2755757999536916, -3.2449160187036132, -1.471991606945889, 0.26842941960635, -0.45148917096807006, -0.516781425115903, 1.0069859881882677, 0.6915450751070147, -1.1015696148060465, -0.13567687006489693, 2.4070815690592973, 1.46820035635726, -1.2678457058753572, -0.22806303391949267, 2.062505098114211, -0.8553620994467543, -5.463714056105411, -3.225573108652955, 2.8981310872431827, 2.6050796533386116, -3.1882454890746295, -4.171517424174301, 0.6916278707964699, 2.559367003549965, -0.477015573427062, -1.6012752752952906, 0.6906532102701619, 1.1792351442500233, -0.6707653149380413, -0.7947914434550899, 0.06544412391601152, -1.4521252934471323, -3.061683737578305, -1.1080561853374502, 1.4824352374631837, 0.7493028912857368, -0.7831027757069547, -0.17575803576124147, -0.033326222662232945, -1.3283383864004552, 0.32048660731000617, 4.797095954227537, 4.970323196702274, -0.14823593969252993, -2.3782085078056574, 0.17006399879512518, -0.9461490539828533, -7.584146002952826, -9.826643440263918, -3.906194296022387, 0.6674894145540109, -1.6584723621260085, -3.8119886433891295, -0.88129207019924, 1.608162686279835, 0.003142651962954111, -1.0487139005168582, 0.7509278723506574, 1.2626346302416187, -0.4318311661955246, -0.345008709703192, 1.3140388739886053, 0.7316667909474729, -0.7582673662295212, 0.5967664477606265, 2.4270094833150537, 0.8495010445705091, -1.2366502555528467, -0.2549594281254257, 0.5885905855025816, -0.881922604817282, 0.1498176154614002, 4.65583727345839, 4.512565248855882, -2.6263990919181017, -6.356365078618268, -1.0105325628245527, 4.075082481376577, 1.4580690805746757, -2.1800342751962773, -0.44678048909510315, 1.2067527118297445, -1.9905828949212805, -4.461376084647307, -1.9252620308199384, 0.6651391654686554, -0.19846411319528023, -0.6559117392924569, 0.959843565562579, 0.9011030081229465, -1.007007804047495, -0.9110625169558089, 0.2573211147742632, -1.1725148943333836, -2.9177177256263787, -1.0871933327364607, 1.2331638596447885, 0.23230959034017598, -0.56731186760933, 1.6294235751321198, 2.071572059451078, -0.8526005248754468, 0.06596338328391217, 6.420532575188079, 7.966631893297108, 0.5165136704314726, -5.115360222029939, -1.7385558418667735, 2.5218441716373423, 0.5249061146530715, -2.050129266394781, -0.06823693801282806, 1.5342625826581142, -0.5770460811452205, -1.6027992933849207, 0.3537811448651078, 0.48104622296797517, -1.9903236385735743, -2.2412934644299884, -0.1168075621649092, 0.2716767994593092, -0.36167789413700235, 0.8423071412116154, 1.2965234511028891, -1.3800144295197574, -2.7383820544955735, -0.0512456683509486, 1.5157806222113537, -0.4755445314746732, -0.4659470927327839, 2.7597520693837003, 2.552756335335683, -0.751378254087301, 2.0493123122941506, 10.461119998176697, 11.947324034684566, 3.5195660548043457, -2.8842656548978436, -1.1862135820554571, 1.2404337044149605, 0.22467699507872027, 0.7400077925800332, 3.6262905786697197, 3.3413176676389775, 0.11752693527275686, -0.5289022448507524, 0.899589968223267, 0.20141282043874403, -0.9183315623995791, 0.7611737691350137, 2.2139607073062386, 0.6920558983063164, -0.22145180901562234, 1.2534536394508162, 1.2348372490974449, -0.2597687613178276, 1.666407928944217, 5.233062967886905, 3.782972586233586, -0.18709140369655475, 1.2212802191605525, 5.171436817284961, 3.273299531291659, -0.7406179842416376, 2.5011006761461783, 8.729131546552303, 6.817392124380277, -0.7280727277347739, -3.0196406057665888, -0.12630281010389127, 0.3677084188138471, -1.2551763807657625, -0.532523972453041, 0.3569093317769869, -1.520379873395125, -2.3470040635528853, 0.16114896647795826, 1.379229437667195, -0.5634975726346662, -1.2802036297798112, 0.06606398036367273, -0.22119155103594915, -1.032644218138166, 1.1439821569835964, 3.137928477783184, 1.0689354330661243, -0.6227418333241661, 1.543934738193247, 1.3864164866512623, -4.148291938497587, -6.281381508221282, -0.6790188151214667, 2.734069451080997, -1.9922618593421486, -5.673823006815132, -2.046296037804358, 0.9771306835159588, -1.9860721591523234, -3.946480226815013, -0.7136349713627236, 1.538841418819768, -0.20895498420789405, -1.0526789856172196, 0.2244899532590443, -0.17533145275168352, -1.193069481905281, 0.6195836656646992, 2.359007246705625], 'positive_zeros': ['0.5436443816034383996967835394', '1.92333836634974556529788562340', '2.43923191435523843710992678810', '3.6621751295980486788824540198', '4.76529868606314840777845152454', '5.67261988961574228423965040321', '6.903539559311591654109324418687', '7.543745853393237460939405756010', '8.422247919847254156566114581383', '8.899069107939451541008139816201', '10.13589907507390602365760310169', '10.61858826544613554844454283329', '11.35411637914446711027760371501', '12.29369942675706725562918454908', '12.824466563508001230125958176459', '14.13381949725939144276817722439', '14.81128207125013537546688651125', '15.6841508905846260504191149971', '16.54333331263685557032303651228', '17.1805563383162826439771694510', '17.91554286334992514960215538691', '18.61273082261486679198694859611', '19.22415328335123023166477337138', '20.1230591902629837795392894061', '20.915362342212846906173141911319', '21.30779155853360007988601537222', '22.11965674772086760505206958640', '23.28254147516307674440340383239', '24.12682108217996134944949454113', '24.643249994438246630998355868620', '25.44037068381297882967936992036', '26.35950766172966548783773424438', '26.85770392828251382726165414337', '27.45438966852408206866927036503', '28.2827092801989914255398859102', '28.87358420600555530235517245336', '29.69339681228358709547070913461', '30.17380895985377191131573014562', '31.2275804857155831773691306029', '31.51973187469151800004930592901', '32.72886348735110551898374478791', '33.71926875598241291258380379781', '34.13508729615961953128853643804', '34.60702688396686864833287432237', '35.56418603272510473869099979448', '36.35085005404386064834789522233', '36.91437762362039417543492148345', '37.240149905663978487575318338218', '38.26945917235085129637511385311', '38.78931533759813412199604146843', '39.59480436698994018193176929813', '40.12882508586049436803966395041', '40.94273110961166260608021566453', '41.90589578781331720949474114288', '42.62611953240679910421860474940', '43.29530339278823532455725582337', '43.98012797297090293722276039756', '44.61106078528242131709832729267', '45.00319252257808372649937792380', '46.16553428605369213889939544499', '46.53832179978865486889270700494', '47.07104809083770769340124867592', '47.70747230856297134764124349537', '48.63534095193265715777151159096', '49.09901312792213659516526395546', '49.95944158435632917920439779887', '50.715988020521834706197973317259', '51.45510631009777618322118960735', '52.334884132988082081775423290496', '52.90790803890199142349858391850', '53.31233479581983411150506012620', '54.21265712667400801649021443466', '54.57804015642396752239984337367', '55.651841983203842035583773249182', '55.88152682205935792069213287672', '56.6284709566014834288186763333', '57.36557325060578728682657223496', '57.792540049297452491995853869933', '58.73631359321458025680767479484', '59.464492640270477145242474002291', '60.28201805891902016078838576813', '60.883999905643113173683201124890', '61.523565468636195714415069346760', '62.32357361940090753736768760942', '62.90626366797925778490994724276', '63.51941552149398266490529658819', '63.78056465685031797417186062933', '64.90705994143107277461804227413', '65.38766327785923431390864729869', '65.98624720828633038472567074542', '66.541639642520488393073412800248', '67.09534995546330130193087873261', '68.23490127153563696656636856022', '68.67163821588600794990614168753', '69.51914681885866130197857629488', '70.362264390474963887656796444283', '70.6801827821889106778898685652', '71.38375868116496149954440986398', '72.24708762936795832703169860370', '72.66608036623165954810446064715', '73.24408855704654604787830738929', '73.86559140819417698732974801305', '74.50603860154715274263882446074', '75.28179850552765290071313766547', '75.89726829744302685835667150408', '76.27445016465792473980685540715', '77.00084494634562151081206060226', '78.28094304686227512907699635203', '78.749801461821308172893315136892', '79.03919583387946841467373649715', '80.11041360014733471690811259291', '80.467432552567825388363701843702', '81.25109611413051991267542424761', '81.8042959208158775120868337119', '82.34578742558582160539359757241', '83.12098039123389963987239390058', '83.476637307129738995448321410588', '84.2102212205535014669486380478', '85.037389066297476669747411435969', '85.45099782280345572867762727831', '86.07186300703861036799989285901', '87.14216748625194539440923163712', '87.598140628749745229556650476942', '88.68414804361289201298197759976', '88.84217777809043524355958881035', '89.4270458617538630182615080000', '90.18155047114372295085883708509', '90.985051416052598584020808303166', '91.27606515958441538198795208426', '92.16411581147479003920370958354', '92.49057589150213311065002806497', '93.08878372197299142476661263294', '93.96347639149199351729442098834', '94.45580957506836908081984362205', '95.19848870208124961920546156425', '95.7833154922806214538885192979', '96.774448514345625600358872252805', '97.28365343764721996592935808254', '98.018930060535247636150716826858', '98.44423516309457034631489784955', '99.0590116258393380425068422057', '99.7682890715035764962299171753', '100.346372311846836484434164054417', '100.80362677166413960844958435825', '101.665688190310275918805168438437', '102.23130903235028240669939730113', '102.47622067048030076952807681497', '103.2788525703863814697800154432', '104.12859380564842651169968642349', '104.89406517359859394949604503668', '105.31113625525932777600418097559', '106.12256928674002585142801170886', '106.875060037979315679257957716432', '107.440680569125416198289637007304', '107.9916198116265767827473959303', '108.43810900253114770610294471691', '109.11207519309223029729812541948', '109.85153601336953702483576026319', '110.36189266935800517024021275078', '110.98001396769175988478604677455', '111.39195318651462519821643307849', '112.35354888715010582604262027143', '112.61386844763282604201170907912', '113.38904424445759828800740390806', '114.50765654149831833297506034642', '114.94314382985360559952235515350', '115.38340042073177103853424715438', '116.067319070096380253562675442400', '116.97259445419486155812949715285', '117.40763066505236891164614859196', '117.7763699047149924505883417146', '118.57022697393407726130897934694', '118.98562705308265633331249506519', '119.74913883252845769649972716684', '120.483108944323021524856959838103', '120.79334513615272615967360066057', '121.40706653758338479844178039619', '122.12639548164086720786439219475', '122.920083267509593931275750038181', '123.76963317159633241110591390220', '124.17398344097758146369465605193', '124.98039820450295770267639820870', '125.31983720658108939357074351180', '126.09927114413240059138449798549', '126.652782062758973355898662238195', '127.37656504062051662986436851139', '127.73107839201004945813612843222', '128.28514577325979545396676244156', '129.11967694091652592680286263195', '129.43873099483427127927415157554', '130.36986383308522686829382570032', '130.73150521173190121331940111787', '131.32428975727353689141600230886', '132.28021760013384659841373161057', '132.88404724830125640417206778466', '133.70034937382346545224514562418', '134.20728917135850461564505431260', '134.5042310311218361746151941495', '135.19604784575093620404336493871', '136.14991750248929736237739094348', '136.43512135547755598606829268837', '136.98701852701875025300026720454', '137.6102218220574991648033293815', '138.140787434601507883744697757006', '138.89627438975739616755892064823', '139.398789855242536327355217083617', '139.94791958316129049070591458610', '140.77829218594847532257606961487', '141.39368018844340227565939185685', '142.144357164532958149560337478485', '142.76821720027493920871785566821', '143.349718837057824268938618676062', '143.947552311825013039141264829511', '144.60864982658962296981835834529', '144.7417093059882053276210683238', '145.731520053499079563812306822403', '146.36719567720807039841433547187', '146.93220818563719080083110715001', '147.176980292224192798405994613603', '147.78603114774596034022264623756', '148.74100618373665767960964664520', '149.35265036214763729217527188153', '149.61435735118719548279025095175', '150.83899876944062691020010659513', '151.10651001520825063732369572598', '151.94602857884274016237031636053', '152.50041641517813571465701109354', '153.01406633459660497283601870453', '153.66792076694852928327078643240', '154.12635284801577608694437193354', '154.8069358107664139154753940272', '155.23387359542701551778746066355', '156.03256784021185376686271335732', '156.6073321330556631866985293407', '157.02020879348488391893953352009', '157.48660898884355601128312579759', '158.334235870205598345841044747175', '159.105395222605853481913057920763', '159.779789199957253384715646699440', '160.35660661768244252985607201633', '160.78535276839687907044564699639', '161.74456467901419130607466810486', '162.14757661194137058979398260632', '162.64070204331925894687543433637', '163.26965128730291368412482851224', '163.94644424002934208442773058176', '164.19650020253367949313134159234', '165.11098361003573223690003903132', '165.66369338177633393110897021414', '166.04854440407447387411576902494', '166.78277557224308969940842824037', '167.18301754310521634347002675007', '168.14328506325894068385362035602', '168.84360825955520033400566719503', '169.41736833591618811862821991349', '170.00701818079287829941145235798', '170.55807709095192983942628686669', '171.19641376080636462057749504691', '171.6331096233158013824332906221', '172.522024784271308625930809589507', '172.9071984422527722169652037343', '173.27226619958731195080421239426', '173.926855958765178131687848309198', '174.69241798992915907286428360165', '175.24728563215420278511724566952', '175.67844228652464041096817722907', '176.46987966174281106274286570300', '176.76430167735509686383074118607', '177.93770947050521996694144662865', '178.5424585636924922695426111169', '179.14163313311559342429508354073', '179.223296283177925236259000028988', '180.32692497731722307767363440690', '180.73506394524203487316332625096', '181.28596412349488424584474988649', '181.77597804638019127903253057011', '182.62267237897943259312745694247', '182.88403746141851126731619378134', '183.66170259840448163559144115922', '183.88406312008768410920292181379', '184.97485496880150464684913896329', '185.20456603324371027362374941235', '186.15482277054699478835502685793', '186.42112870359276637914401302996', '187.46544750841729864887223403836', '188.14066100664882341066626450460', '188.50554854674411836402884156657', '189.16505264037883034336394882334', '189.47306756438298239155991026384', '190.29494732825609864288372709608', '190.859791013818384751891809220773', '191.54297433345531384426622014003', '191.81806531748092193290090842434', '192.38080434106226640296774804862', '193.24273917236981142497708040914', '193.56787023742223307789587522965', '194.15950071495584279123773189639', '195.032468803149321579479933850837', '195.52670506463896044351775435386', '196.38836439961280653064630304278', '196.71792172364955189264325181407', '197.557360241769817340729998168326', '198.09619677309550356925464785836', '198.68742387859475428093100392863', '199.023350677980130023503282074915', '199.615746760576511191728396773100'], 'prelabel': '1-1275-1275.548-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.9210751072791314, 'root_angle': -0.17449478259434234, 'root_number': '0.456816596099907635419454982668-0.889560901528216814498660472573*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.174494782594', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(20)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.693513724444317649886980482999-0.131637923606550422005521132525*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.543644381603', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.92333836635', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.43923191436', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 5.9210751072791314, 'bad_primes': [3, 5, 17], 'central_character': '1275.548', 'conductor': 1275, 'conductor_radical': 255, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1275/548'], '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': '1-1275-1275.548-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': '1-1275-1275.548-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.9210751072791314, 'root_angle': -0.17449478259434234, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.543644381603', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1275.548', 'Lhash_array': ['dirichlet_L_1275.548'], 'factors': ['1-1275-1275.548-r0-0-0'], 'label': '1-1275-1275.548-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1275/548'}
Lfunction data - 1-1275-1275.548-r0-0-0