-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1565312592878522999718380542991', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [0.5176380902050415, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.9418619641550123, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [1297, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 1297], 'central_character': '3891.3890', 'coefficient_field': 'CDF', 'conductor': 3891, 'conductor_radical': 3891, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-0.5176380902050415, 0], [1.0, 0]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [1.9318516525781366, 0], [1.0, 0]], [[1.0, 0], [-1.7320508075688772, 0], [1.0, 0]], [[1.0, 0], [-1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.9318516525781366, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [1.7320508075688772, 0], [1.0, 0]], [[1.0, 0], [1.7320508075688772, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0.5176380902050415, 0], [1.0, 0]], [[1.0, 0], [1.9318516525781366, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.9318516525781366, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0.5176380902050415, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [-1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.9318516525781366, 0], [1.0, 0]], [[1.0, 0], [-1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0.5176380902050415, 0], [1.0, 0]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [-0.5176380902050415, 0], [1.0, 0]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.9318516525781366, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.9318516525781366, 0], [1.0, 0]], [[1.0, 0], [1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [-0.5176380902050415, 0], [1.0, 0]], [[1.0, 0], [0.5176380902050415, 0], [1.0, 0]], [[1.0, 0], [-1.7320508075688772, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0.5176380902050415, 0], [1.0, 0]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [0.5176380902050415, 0], [1.0, 0]], [[1.0, 0], [-1.7320508075688772, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0.5176380902050415, 0], [1.0, 0]], [[1.0, 0], [2.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.7320508075688772, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [1.9318516525781366, 0], [1.0, 0]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.5176380902050415, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.7320508075688772, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.5176380902050415, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.5176380902050415, 0], [1.0, 0]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [2.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0.5176380902050415, 0], [1.0, 0]], [[1.0, 0], [1.9318516525781366, 0], [1.0, 0]], [[1.0, 0], [-1.9318516525781366, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.7320508075688772, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.7320508075688772, 0], [1.0, 0]], [[1.0, 0], [-1.9318516525781366, 0], [1.0, 0]], [[1.0, 0], [-1.7320508075688772, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.7320508075688772, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.7320508075688772, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.9318516525781366, 0], [1.0, 0]], [[1.0, 0], [1.7320508075688772, 0], [1.0, 0]], [[1.0, 0], [1.9318516525781366, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.7320508075688772, 0], [1.0, 0]], [[1.0, 0], [0.5176380902050415, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.9318516525781366, 0], [1.0, 0]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.9318516525781366, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.7320508075688772, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.7320508075688772, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0.5176380902050415, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [-0.5176380902050415, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.7320508075688772, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0.5176380902050415, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.9318516525781366, 0], [1.0, 0]], [[1.0, 0], [-2.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-2.0, 0], [1.0, 0]], [[1.0, 0], [1.9318516525781366, 0], [1.0, 0]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [-1.9318516525781366, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.7320508075688772, 0], [1.0, 0]], [[1.0, 0], [-2.0, 0], [1.0, 0]], [[1.0, 0], [-0.5176380902050415, 0], [1.0, 0]], [[1.0, 0], [-1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [-1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.7320508075688772, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.9318516525781366, 0], [1.0, 0]], [[1.0, 0], [-2.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-3891-3891.3890-c0-0-10', 'leading_term': '1.53070511054470068856201910713', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3891/1/c/f/3890/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.5307051105447007, 1.5348356531192549, 1.5467777439175734, 1.5652371255576085, 1.5882223220510479, 1.613246728661051, 1.6375418446300678, 1.658249105924175, 1.6725746851002286, 1.67790581278094, 1.6718951037383418, 1.6525217291972571, 1.6181373257007907, 1.5675022872621005, 1.4998157583251917, 1.4147407464294097, 1.3124244198865256, 1.1935127875690443, 1.0591584682135202, 0.911020045923128, 0.7512515004514998, 0.5824803416477965, 0.4077733304794006, 0.23058900883357766, 0.05471666784316919, -0.11579815598011553, -0.2767410706432024, -0.42382799902979273, -0.5528144978312437, -0.6596130766029931, -0.7404158793432031, -0.7918196475680486, -0.8109495047298141, -0.795577805199778, -0.744234094111286, -0.656302142585737, -0.5321000692222925, -0.3729397429877671, -0.18116199066782512, 0.03985539479560289, 0.28571923407753225, 0.5510737711268234, 0.8296854892005204, 1.1145597464262849, 1.398088007895951, 1.6722233724078295, 1.9286810045376337, 2.1591590241201355, 2.3555744149462803, 2.5103076327917324, 2.6164488594023587, 2.6680383011735476, 2.660292602575112, 2.589809363106812, 2.4547419340413614, 2.2549371404821685, 1.992029328977389, 1.6694851744417127, 1.2925949749545054, 0.8684076906378718, 0.40560870403955224, -0.08565885501420853, -0.5940264254167411, -1.1071812044856733, -1.6121895217013003, -2.0958539077934613, -2.5450937688032433, -2.947338241545154, -3.29091880773212, -3.5654486358756277, -3.7621754485164423, -3.8742950090026067, -3.897213102411506, -3.828745147026226, -3.6692442949032316, -3.4216510222068455, -3.0914597130692694, -2.686600528148514, -2.2172378286586616, -1.695489493561641, -1.1350745077273212, -0.5508990929497771, 0.041405718042634036, 0.6259799174977189, 1.187246861889674, 1.7104240278139653, 2.1820135702066628, 2.5902542436519327, 2.9255171493300023, 3.1806293940133736, 3.35111205884625, 3.435321809775515, 3.434488944879082, 3.3526485464872704, 3.1964655453005744, 2.9749587493718073, 2.699133070848856, 2.3815331209072466, 2.0357348640163377, 1.6757949624714228, 1.315679654722304, 0.9686963752492551, 0.6469517499577336, 0.3608590366399828, 0.11871651335195813, -0.07362421964860554, -0.2129844907206796, -0.29896803514036874, -0.3339472029578228, -0.3229246534186622, -0.2732747573939861, -0.19437436708623815, -0.0971377792691364, 0.006524627074897317, 0.10430068337282972, 0.1840972875126167, 0.23465959568768824, 0.24615969541156596, 0.2107265830692587, 0.12289126593520984, -0.020075923244190247, -0.21795427909813914, -0.46750099449046656, -0.7625255922519435, -1.0941106386357446, -1.4509719212327956, -1.819944439504297, -2.186574151811384, -2.535789767476227, -2.852624260945786, -3.1229524737538457, -3.3342093623055153, -3.4760532846809826, -3.5409402630665245, -3.5245783956416825, -3.426236426079459, -3.2488867327339226, -2.999170420230305, -2.687180464701061, -2.3260676085212655, -1.931482512442997, -1.5208761256251722, -1.1126879023242966, -0.725457976041507, -0.376904339425986, -0.08300917586589379, 0.14284046900945194, 0.2906136226856713, 0.3542572059540814, 0.33214345451638827, 0.22731500849942282, 0.04750870013168708, -0.1950507402612896, -0.48408488550423623, -0.7999103423660179, -1.120277727084995, -1.4213665383725351, -1.678892887443712, -1.8692801940648833, -1.9708383463720138, -1.9648947477207208, -1.8368213159434787, -1.5769049084898135, -1.1810147331915979, -0.6510288438817475, 0.005007542175371664, 0.7730069031179511, 1.6332491200857377, 2.561063956148386, 3.5277607302933687, 4.501767043754657, 5.449927434270406, 6.338904026078011, 7.136615103471126, 7.813644434099132, 8.344554329621385, 8.709038919254073, 8.892860820746508, 8.888524050253913, 8.695648186525794, 8.321022925657484, 7.778337547353563, 7.0875956994100795, 6.274241489457691, 5.368037347124363, 4.401746722988004, 3.409684743670534, 2.42620688702832, 1.4842091729039113, 0.6137130568233532, -0.15939586614827858, -0.8144139252747036, -1.336599711809296, -1.7176518270038805, -1.955862815827911, -2.0559448964655553, -2.0285402373643286, -1.889445064039972, -1.6585918990678779, -1.3588469227912368, -1.0146890781785858, -0.650843578078036, -0.2909445455160145, 0.043700518713371474, 0.33517781176285055, 0.5698090051924388, 0.7387238694050061, 0.8381353800279991, 0.8693060678331269, 0.8382121822120918, 0.7549297163292956, 0.632782484584229, 0.4873063082474654, 0.3350941301881701, 0.19259388985557818, 0.07493379948189204, -0.005151935344072571, -0.03822986557803949, -0.01884944835899707, 0.05404295031840529, 0.17698547505388967, 0.34218681514322896, 0.5380072108604019, 0.7497063226950516, 0.960412873067659, 1.152256521727204, 1.307591434537387, 1.410234173861486, 1.4466363627211551, 1.4069152682045132, 1.2856729361571955, 1.0825464215730156, 0.8024473545551775, 0.455467675106333, 0.056448782061418186, -0.3757676401436241, -0.8193685034295881, -1.2508208739181434, -1.646273855406219, -1.983027241225231, -2.2409770609605744, -2.4039472224316545, -2.4608210953475513, -2.406396947051452, -2.2419061342648527, -1.9751520768866822, -1.6202502190228776, -1.196973135077774, -0.72972924307947, -0.24622676672435131, 0.2241048007887216, 0.651846753994755, 1.0093760531710934, 1.2725964347500338, 1.4225096103047203, 1.4465273101039242, 1.3394380140922788], 'positive_zeros': ['1.23481390897200077080695284226500', '1.97174844217297154998158521473678', '3.08896125901124138345973133422207', '4.16050675858512346041414621404501', '5.31092611731364447331794751751933', '5.73506298856109246962553118442747', '6.08765989855090536381342941422029', '7.38012194847607403518738366386660', '7.67892158602701574421415072372297', '8.378550331570780564433528553181405'], 'prelabel': '2-3891-3891.3890-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3935070735934614, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.23481390897200077080695284226', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.97174844217297154998158521474', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.08896125901124138345973133422', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.9418619641550123, 'bad_primes': [3, 1297], 'central_character': '3891.3890', 'conductor': 3891, 'conductor_radical': 3891, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3891/1/c/f/3890/3'], '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': '2-3891-3891.3890-c0-0-10', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3891-3891.3890-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3935070735934614, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.23481390897200077080695284226', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1565312592878522999718380542991', 'Lhash_array': ['1565312592878522999718380542991'], 'label': '2-3891-3891.3890-c0-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3891/1/c/f/3890/3'}