-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1712301402270859237133089315557', 'a10': [-2.1536338936814046, 3.730203324758582], 'a2': [-1.3575663996956382, 2.3513739789212034], 'a3': [0, 0], 'a4': [-2.6859730591651543, -4.652241806235253], 'a5': [1.5863930443212517, 0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [9.155281503658717, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.5642081874154, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '1323.361', 'coefficient_field': 'CDF', 'conductor': 1323, 'conductor_radical': 21, 'conjugate': '704491431080593353999524770194', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.3575663996956382, -2.3513739789212034], [-1.0, -1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.5863930443212517, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.3487521826062043, 0], [11.0, 0]], [[1.0, 0], [-1.5891617419647213, 2.7525088785275593], [-6.5, -11.258330249197702]], [[1.0, 0], [-1.4002683034259225, 2.4253358457619707], [-8.5, -14.722431864335457]], [[1.0, 0], [0.31284640947635045, 0.5418658761785364], [-9.5, 16.454482671904334]], [[1.0, 0], [-0.2848672006087237, 0], [23.0, 0]], [[1.0, 0], [2.273959843364261, 3.938613983078266], [-14.5, 25.11473670974872]], [[1.0, 0], [3.71502366190382, 6.434609733737999], [-15.5, 26.846787517317598]], [[1.0, 0], [4.011258169961107, 6.947702952648392], [-18.5, 32.04293994002423]], [[1.0, 0], [5.013289263466821, -8.68327171736409], [-20.5, -35.50704155516198]], [[1.0, 0], [3.129367441090073, 5.420223403519812], [-21.5, 37.239092362730865]], [[1.0, 0], [-5.573826011300163, 9.654149844120862], [-23.5, -40.703193977868615]], [[1.0, 0], [-1.3934876967330858, 2.413591490463836], [-26.5, -45.89934640057525]], [[1.0, 0], [-2.2873439731699725, -3.9617959759168557], [-29.5, 51.09549882328188]], [[1.0, 0], [-0.192506979306761, 0.33343186897092053], [-30.5, -52.827549630850754]], [[1.0, 0], [-1.269579615496531, -2.198976398293752], [-33.5, 58.023702053557386]], [[1.0, 0], [-1.4520803132714777, 0], [71.0, 0]], [[1.0, 0], [-0.23406694252519802, 0.40541583682594723], [-36.5, -63.21985447626402]], [[1.0, 0], [-7.856203350035119, 13.607343356853647], [-39.5, -68.41600689897065]], [[1.0, 0], [-6.993382145754514, -12.112893193191873], [-41.5, 71.88010851410841]], [[1.0, 0], [1.2935292019778608, 2.240458298899679], [-44.5, 77.07626093681505]], [[1.0, 0], [-7.229623897981838, -12.522075910918698], [-48.5, 84.00446416709055]], [[1.0, 0], [9.837762290015124, 0], [101.0, 0]], [[1.0, 0], [-11.057948740858286, 0], [103.0, 0]], [[1.0, 0], [0.9621532095550779, 1.6664982436148599], [-53.5, 92.66471820493493]], [[1.0, 0], [-9.30340777237895, 16.11397494529153], [-54.5, -94.39676901250381]], [[1.0, 0], [1.5933835201245479, -2.7598212127986637], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 22, 'label': '2-1323-63.4-c1-0-22', 'leading_term': '0.892091892145405770358652914813199930623782408954138377', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1323/2/g/h/361/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.8920918921454057, 0.9373783806835468, 0.9749869954559383, 1.0050300457598782, 1.0274777683165757, 1.042174290239986, 1.0488648330242152, 1.0472317143696512, 1.0369363973792665, 1.0176648160617947, 0.9891733975292554, 0.9513335132238082, 0.9041724418986731, 0.8479092585759777, 0.7829843473218578, 0.710081466325807, 0.6301414822378577, 0.5443670555744392, 0.45421772027738916, 0.36139497562573186, 0.267817210397783, 0.17558451482424206, 0.08693370757286267, 0.0041842101557402435, -0.07032426689272751, -0.13430091293880045, -0.18557821519323375, -0.22218955715257452, -0.242447693156259, -0.24502150223921132, -0.2290082123676717, -0.19399815072338267, -0.14012903194030865, -0.06812685701739707, 0.02066932886490667, 0.12430127462849047, 0.24020599225151773, 0.36525234919428684, 0.4958006214935688, 0.6277850882061148, 0.7568189088852478, 0.8783196280819953, 0.9876527232272538, 1.0802896877559822, 1.1519762564970453, 1.1989055739927574, 1.2178904182936405, 1.2065280620578867, 1.163351016344265, 1.087956793135031, 0.9811099673289595, 0.8448102370986752, 0.6823208833489323, 0.4981530142667016, 0.29800223777996776, 0.08863590907633463, -0.12226918431673357, -0.3263369596321005, -0.5147462775956534, -0.6785235491239462, -0.8088660079170087, -0.8974861060617535, -0.936965861736381, -0.9211086570307361, -0.8452750292422997, -0.7066884917708975, -0.5046974196793449, -0.24097958306103426, 0.08032296751837333, 0.4525492628357455, 0.8665533731740739, 1.310832554061832, 1.7717519764206198, 2.233864902059631, 2.680323404937334, 3.0933708889718243, 3.4549038642506784, 3.7470868741390038, 3.9530012778108965, 4.057305944134243, 4.04688595072429, 3.911464235382334, 3.644150920092106, 3.2419057929547996, 2.7058912268205533, 2.0416956298489293, 1.2594113140540186, 0.3735553396948898, -0.5971726908349432, -1.6302959337936012, -2.7001224083536512, -3.7784511663186775, -4.8354034925615075, -5.8403542259957435, -6.76293310604303, -7.574061810867554, -8.246989290696364, -8.758286304175146, -9.088759881256323, -9.22424984816819, -9.156272579266737, -8.882481738232324, -8.406921817184767, -7.740057587245714, -6.8985708834388015, -5.904925149415564, -4.786707506610419, -3.575767399714596, -2.3071797019892, -1.0180681383304977, 0.25366837963236, 1.4706787552646425, 2.597481001556042, 3.6017295679433743, 4.455377423982769, 5.135684842848224, 5.626032208836222, 5.916501545282759, 6.004200552842975, 5.893313404234593, 5.594873926137355, 5.1262686201475605, 4.510488704395771, 3.775161455274829, 2.9514010676782974, 2.0725275445348164, 1.1727083489468986, 0.28558136881003954, -0.5570810751642459, -1.3266090098985062, -1.9985184953474115, -2.553395182396876, -2.9775398435650215, -3.2633489874145405, -3.409416050188425, -3.4203518275950557, -3.3063361289776223, -3.0824254478032937, -2.7676531016129644, -2.383968202591538, -1.9550674564361739, -1.5051787392945848, -1.0578573888810785, -0.6348550346002858, -0.255116610668283, 0.06604586409234905, 0.31756375031114514, 0.4929791486837769, 0.5905548969336553, 0.6131267849730947, 0.5677114261254198, 0.4648963397223014, 0.3180504565539054, 0.14240280123356677, -0.0459560095286772, -0.2310909896710433, -0.3981997380587145, -0.5344929597670667, -0.6299284300578701, -0.6777572103173901, -0.6748522592843489, -0.6218026786332613, -0.5227709388527948, -0.38512472863788455, -0.2188687144877286, -0.03591366845075188, 0.15076962265175703, 0.32805713671023656, 0.48358073982291455, 0.6065810669456942, 0.6886489624682203, 0.724307143691357, 0.7113937043546189, 0.651221549651523, 0.5485021081311672, 0.4110368341779004, 0.24919515767565545, 0.07521169741532575, -0.09765218447784481, -0.25602786500247343, -0.38737919193647324, -0.4808993549011824, -0.5283035381016685, -0.52446179939508, -0.4678261892823978, -0.3606189260389267, -0.20876372446117303, -0.021559200352263386, 0.18888941986003158, 0.40844738683969295, 0.6218884991517996, 0.8139342083279976, 0.9703253366628714, 1.0788538424871041, 1.1302826570110136, 1.1190870455472206, 1.043961005678644, 0.908046385843349, 0.7188598818033317, 0.4879127923199614, 0.23003915117750035, -0.037531747350187744, -0.29630372153197676, -0.5277725927183591, -0.7147337139443697, -0.8425498552820059, -0.9002904775860265, -0.881658716321742, -0.7856335397972449, -0.6167710235783265, -0.38512960319202255, -0.1058083087245175, 0.2018871360089244, 0.5156095081747659, 0.8114014236311915, 1.0653066965001343, 1.2550595049383724, 1.3617392049165167, 1.3712757645788463, 1.2756954871747805, 1.0740089624231557, 0.7726625466910821, 0.3855001461664309, -0.0667877541053491, -0.5577177948200683, -1.0565262245664984, -1.53006360195495, -1.9449660877776018, -2.2699742084034646, -2.4782538400568237, -2.5495667555682733, -2.472140244095132, -2.244097325353629, -1.8743305700056334, -1.382732515280234, -0.799732550004623, -0.16513184887575566, 0.4737280158971609, 1.0643834889959856, 1.5521346869046622, 1.8832438968531648, 2.0082662098940456, 1.8853155369506556, 1.4830648749327209, 0.7832876588367356, -0.2172327174289613, -1.5055664599701797, -3.0523737804360516, -4.812564902531478, -6.7268807091199445, -8.724335862038197, -10.725412922149085, -12.645847964467068, -14.400808548089266, -15.909236338750075, -17.098111235647757, -17.906392786798147], 'positive_zeros': ['1.35076763420659789725733554150452', '1.97943294727964566246097478280026', '3.24720288693353955682497884710972', '3.97061386944087834012035992373748', '5.12074539032295755948056879921450', '6.43347651516657076783975494620077', '7.46081821652526103060523490006992', '8.483000289914366045436945124475297', '9.009234451627173536322121404098293', '9.679203654176516501595990018488978'], 'prelabel': '2-1323-63.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.250262787439717, 'root_angle': -0.08945864114118414, 'root_number': '0.9607667849024274554799327371604717462555286673490431427 - 0.2773575040056653934917086037748426310556251503046175258*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.04472932057059207', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.35076763420659789725733554150', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.97943294727964566246097478280', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.24720288693353955682497884711', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 10.5642081874154, 'bad_primes': [3, 7], 'central_character': '63.4', 'conductor': 1323, 'conductor_radical': 21, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1323/2/g/h/361/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-1323-63.4-c1-0-22', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1323-63.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.250262787439717, 'root_angle': -0.04472932057059207, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.35076763420659789725733554150', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1712301402270859237133089315557', 'Lhash_array': ['1712301402270859237133089315557'], 'label': '2-1323-63.4-c1-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1323/2/g/h/361/1'}