-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2723567456302068124766044916101', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.25662650597030207, 0.054547647742438816], 'a4': [0.0, 0.0], 'a5': [0.12147746181066692, -1.1557808446405908], 'a6': [0.0, 0.0], 'a7': [-1.1286442571181747, -2.3929400621148376], 'a8': [0.0, 0.0], 'a9': [-2.6777546552355105, -1.1922131847293187], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.459392382255437, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.1286442571181747, 2.3929400621148376]]], [11, [[1.0, 0], [-2.4752035891013295, 2.2075704275288475]]]], 'bad_primes': [2, 7, 11], 'central_character': '308.25', 'coefficient_field': 'CDF', 'conductor': 308, 'conductor_radical': 154, 'conjugate': '1222200415289281267090386793591', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.25662650597030207, -0.054547647742438816], [2.7406363729278027, 1.2202099292274007]], [[1.0, 0], [-0.12147746181066692, 1.1557808446405908], [-4.8907380036690284, -1.0395584540887968]], [[1.0, 0], [1.1286442571181747, 2.3929400621148376]], [[1.0, 0], [-2.4752035891013295, 2.2075704275288475]], [[1.0, 0], [-3.8582183736840836, 2.8031597308131664], [4.017220926874317, -12.363734711836996]], [[1.0, 0], [-1.0663225684901172, 0.4747573952836764], [11.37522030810059, -12.633462033115702]], [[1.0, 0], [3.6846750707726215, -4.092246246679216], [-1.986040802085416, -18.895916011997194]], [[1.0, 0], [-0.30647291466894605, -0.5308266593503357], [-11.5, 19.91858428704209]], [[1.0, 0], [0.6894106778966549, -2.121787893715366], [-23.461492836873475, -17.04577231648172]], [[1.0, 0], [0.44534874075329317, 4.237210228755922], [-30.322575622747976, 6.445262415350539]], [[1.0, 0], [-10.733906427903062, 2.281562243602824], [33.80118193277623, -15.049255793804608]], [[1.0, 0], [1.7664761022062117, 5.436654418573568], [-33.16969676937284, 24.099195343991397]], [[1.0, 0], [3.2886514120438357, 0], [43.0, 0]], [[1.0, 0], [8.140258635476508, -9.04067311450662], [-4.912837773579713, -46.74252908230885]], [[1.0, 0], [-1.1548779267192792, -10.987929494944186], [-51.8418228388917, 11.019319613341246]], [[1.0, 0], [-3.4324945652489682, -3.812171421248694], [-6.167179332791555, 58.67679182672813]], [[1.0, 0], [-0.8973605909099339, 8.53781570877365], [-59.66700364476215, -12.682613139883319]], [[1.0, 0], [3.5476290515807385, -6.144673763745228], [-33.5, -58.023702053557386]], [[1.0, 0], [-7.176439934905432, -5.21398881238482], [21.940206600621266, 67.52501265695591]], [[1.0, 0], [-1.6591386055854829, -1.8426600991994935], [-7.630577818538703, 72.60009836188395]], [[1.0, 0], [-7.3601497186728215, -3.2769497829186927], [52.861317902349796, 58.70844121271414]], [[1.0, 0], [11.500734352199489, 8.355772610165113], [25.648410533120636, 78.93769085249775]], [[1.0, 0], [-4.693527085331054, -8.12942737849405], [-44.5, 77.07626093681505]], [[1.0, 0], [-6.444872485749952, 4.682473948468965], [29.974648454369902, -92.2524820806299]], [[1.0, 0], [-1.2381275696348182, -11.779996938326512], [-98.79290767411437, 20.999080772593693]], [[1.0, 0], [-3.6180238397062756, 0.7690347074081372], [94.09518213718789, -41.89387423680742]], [[1.0, 0], [6.118248165197162, -6.795002981098715], [-11.18454556963892, -106.41384280440525]], [[1.0, 0], [-9.336043063846459, 16.170500928233075], [-54.5, -94.39676901250381]], [[1.0, 0], [-1.0745213446035553, -3.3070366526297796], [-91.41892036436906, 66.41973350904946]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-308-77.25-c1-0-5', '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/308/2/y/a/25/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.252442766780915, 1.362759671015012, 1.4772197212848128, 1.5952770712883102, 1.7134303170700693, 1.825606589255643, 1.9237546142502642, 1.9985357466595626, 2.0400663977103948, 2.038707887571831, 1.9859083139100362, 1.8750857765361217, 1.702516981955143, 1.4681695556769587, 1.1763958825360552, 0.8363942448039549, 0.46234166213318123, 0.07311375104236431, -0.3084690453940193, -0.656892605701207, -0.9456733206577513, -1.1494750740894488, -1.2464800498350916, -1.22081940179313, -1.0648260160127436, -0.7808466673889278, -0.382351757669923, 0.10588740973589167, 0.6487190727348634, 1.2026983273444223, 1.7192891979291245, 2.1489935030750873, 2.446082711855568, 2.5734903892537027, 2.5073396009182436, 2.2405484115102663, 1.7849899162144705, 1.1717870726498212, 0.4494943587147214, -0.3198543202757786, -1.0665909176649857, -1.7206462989434956, -2.2194321660212086, -2.515466908733819, -2.582773662934278, -2.421133730169839, -2.0574632519191374, -1.5438863543154482, -0.9524759506604368, -0.3670789102296183, 0.12692253363961256, 0.453700201112444, 0.5574810207800991, 0.4109770954738758, 0.020427822803644597, -0.5736903465540261, -1.300685506663486, -2.0681482435907137, -2.7739965089324965, -3.320544047151402, -3.6286545433274093, -3.6498897741002763, -3.3747148250618655, -2.835290551887073, -2.102116775978596, -1.2746955791075751, -0.46733186995616105, 0.20797155541117618, 0.6589806082358384, 0.8282978353648602, 0.7034903054725249, 0.32038819366245086, -0.24132562161082038, -0.8698905439780464, -1.4390163423702194, -1.8285538910361208, -1.9449627248160062, -1.7381016844193282, -1.2113111429765988, -0.4227508312770052, 0.5226316878458864, 1.4895225306316415, 2.3345491968787635, 2.9308045246489836, 3.1903421063706174, 3.08055612100752, 2.6312653151216643, 1.9308559182884273, 1.1117561457716394, 0.32748258352487614, -0.27484776834620245, -0.5816345799073155, -0.5344925374055335, -0.14228441147807763, 0.5191134415574824, 1.3196976820777084, 2.0988663221334534, 2.695460270757035, 2.9787740721599807, 2.8745909771774705, 2.381040425258289, 1.5708720893240136, 0.579284397274354, -0.4207346037761218, -1.251051902163833, -1.7627736878404576, -1.8655684466641507, -1.5459287665800252, -0.8704228396233831, 0.027078413890165975, 0.9719619362549685, 1.7840785199585192, 2.3145112940268393, 2.4762945587890424, 2.2625218932275257, 1.7477554511937652, 1.0720746879270475, 0.41078862056917764, -0.0639995781489077, -0.2218462645713395, -0.0040620119531081566, 0.5613645517426608, 1.3637174746088678, 2.2320526635777, 2.9718188358896187, 3.407905441166273, 3.424744048543622, 2.9944353730991806, 2.186244947284678, 1.1547530179009988, 0.10863274636809585, -0.7335627924221328, -1.1911057121622224, -1.1617140356740476, -0.6457934165548596, 0.25156249727024443, 1.341802665402816, 2.3931245674274844, 3.180975534621605, 3.5376133768059255, 3.389452569775806, 2.773489844446628, 1.8287561101430594, 0.7644534796868473, -0.18810374943214989, -0.8287111380412704, -1.0342273380152551, -0.7863446896871628, -0.17441509046647682, 0.6275695369244256, 1.4045364364262896, 1.9540641657896303, 2.137263935543173, 1.914244875170439, 1.3551439254266182, 0.623548147433685, -0.06409143391578703, -0.49340723452303664, -0.5079706799663459, -0.05204790321074155, 0.8108267972398499, 1.9087686950889047, 3.000005043234414, 3.8299776721121046, 4.193279607635955, 3.9850668486002805, 3.2288667984736463, 2.0733444210430854, 0.7582441798942082, -0.4424946251480407, -1.2865297347709206, -1.6213919226614761, -1.4204621681618748, -0.7873296161932503, 0.07282254359825, 0.9076852260088119, 1.4842389238078968, 1.6499086959883613, 1.372379020019544, 0.7473523526972511, -0.028177505645164226, -0.7104710357241718, -1.0772227467827553, -0.9912769007057992, -0.44259787442873866, 0.4433437624761956, 1.4338808613273932, 2.2475066424268197, 2.627425672139095, 2.411031349358917, 1.576692510830088, 0.25488810344742, -1.3000183765380584, -2.7706392772266883, -3.8545099389036643, -4.338781866496703, -4.151936046941209, -3.378746790400588, -2.2344974004687628, -1.0054311785090972, 0.028374377471671063, 0.6666549464874745, 0.838953936031645, 0.6172643831962342, 0.18797379000527192, -0.208825085562007, -0.35531371575281, -0.1253645887567686, 0.4728405661234109, 1.2938305769237188, 2.0931567049976234, 2.5967841251643016, 2.5821720084686883, 1.9478382058906194, 0.7509627311698137, -0.7987325568459522, -2.3883403658396434, -3.6814903440103706, -4.406604374635518, -4.428957830582998, -3.7859572238783823, -2.6751705613137395, -1.3979668292806802, -0.27435717478639976, 0.4469075036016243, 0.6572684234384766, 0.4163553976528595, -0.06929509521088671, -0.5109262286998588, -0.627063878284953, -0.23177628433375808, 0.7043278014360244, 2.038713577925732, 3.4923351595362813, 4.726165433383315, 5.436928815120772, 5.444196242504663, 4.743218393103994, 3.507696388320146, 2.0413096975328515, 0.691954310959504, -0.24621495370209537, -0.6140769518909684, -0.42813834886862107, 0.13152482457494388, 0.782152063329887, 1.2294233750199661, 1.2609819242239118, 0.8136410295831693, -0.006550234948553479, -0.9578559217888111, -1.739979092609661, -2.091097757950164, -1.874634011536791, -1.1283093418371035, -0.05931790529213871, 1.0140651251413009], 'positive_zeros': ['2.14851588900893797495254432850773', '3.34936020193368494414067672664596', '4.82324831068166884932527266212170', '6.21433439672235401554451307873953', '6.75504683340479367364779701043459', '8.332595179486842026999512494289479', '8.949605912792520924223720513133829', '9.932453185392601013646514420818242', '11.18655372033503100234246088039616', '11.65581278290466887694123002709821'], 'prelabel': '2-308-77.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.568245000711125, 'root_angle': 0.38896190350018256, 'root_number': '0.34180458560051447 + 0.9397710493851471*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.19448095175', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.14851588900893797495254432851', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.34936020193368494414067672665', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.82324831068166884932527266212', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.459392382255437, 'bad_primes': [2, 7, 11], 'central_character': '77.25', 'conductor': 308, 'conductor_radical': 154, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/308/2/y/a/25/1'], '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': '2-308-77.25-c1-0-5', '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': '2-308-77.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.568245000711125, 'root_angle': 0.19448095175009128, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.14851588900893797495254432851', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2723567456302068124766044916101', 'Lhash_array': ['2723567456302068124766044916101'], 'label': '2-308-77.25-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/308/2/y/a/25/1'}